26. Question C.II: MOND works far too well !


First try: Using only Solar System constraints, Newton and then Einstein developed the universal theory of gravitation. This Theory of General Relativity (GR) is then applied to model the universe. In order for it to fit the observational cosmological constraints, inflation, dark matter and dark energy need to be postulated to exist. Tests on scales of 10Mpc and less show this top-down modelling to fail despite major fine-tuning attempts. 

Second try: Using Solar System and galactic constraints Milgrom and then Bekenstein developed a new theory of gravitation. This MOND and TeVeS  approach is now being applied to model the universe. Cold dark matter is not needed, but applications to large-scale structure need to be developed. Tests on scales of 10Mpc and less show this bottom-up modelling to be successful without fine-tuning.

In general it follows that the need for dark matter and perhaps for the other postulates depends on the gravitational theory being used. Since we do not yet understand gravitation it furthermore follows that these postulates probably only express our lack of understanding of cosmological physics.  

Indeed, there is no reasonable astronomical evidence for the existance of cosmologically relevant cold dark matter particles, and so searching for these would be futile.


As introduced in the previous contribution to The Dark Matter Crisis, Question A: Galaxies do not work in LCDM, sociology and majority views, PK was recently contacted by a few people, and here are excerpts from some of the questions asked and the replies. These help to illustrate some of the issues at hand. The questions are

A) So the LCDM model fails on scales smaller than about 8 Mpc?

B1) What is a galaxy?

B2) What is a galaxy? (Addendum on the relaxation time)

C) What are the three best reasons for the failure of the LCDM model?

I: Incompatibility with observations

II: MOND works far too well ! (this contribution)

III: Fundamental theoretical problems

D) What about the Bullet cluster?  And what about the Train-Wreck cluster Abell 520?

E) Why is the main stream community so reluctant to  go along with accepting the failure of LCDM?

This contribution deals with Question C, which may be taken to be central to The Dark Matter Crisis, while upcoming contributions will concentrate on the remaining questions.

The three best reasons for the failure of the LCDM model: 

They can be summarised in three categories. Here is category II. Ctegories I and III can be found in seperate contributions as outlined above.

II)MOND works far too well !

In fact, just as planetary systems are Keplerian objects, galaxies are Milgromian objects.

Milgrom’s discoveryof a0 is likely as epochal as Planck’s discovery of h.


How did the central ideas develop?

A) LCDM was developed top-down. This means that LCDM is an attempt to make the real universe and its constituents fit the General Relativity (GR) field equations which Einstein formulated based only on Solra System data via Newton prior to any cosmological or galactic constraints. It is described by many parameters and these have been measured to high precision so that the LCDM model cannot be adjusted or improved further.

B) MOND has been developed bottom-up. This means that MOND was discovered by Prof. Dr. Mordehai Milgrom (1983) as a description of the dynamics of a few bright disk galaxies then known and of the Solar System. That the conservation laws hold in MOND has been shown by Bekenstein & Milgrom (1984). Since then MOND has been found, without adjustment, to work for very different types of galaxies and on vastly different scales (from the smallest dwarf galaxies to elliptical galaxies to the Local Group and galaxy clusters) and formed the basis of the development of a first new covariant theory (TeVeS) by Prof. Dr. Jacob D. Bekenstein (2004) which cointains Einstein’s GR theory.

MOND thus forms the basis or start of a major new development to understand gravitation and thus cosmological physics. Planck’s discovery of the auxilliary number h (“Hilfsgroesse” in German) was just the same basic discovery ultimately leading to the theory of quantum mechanics.

C) And there are other developments as well: e.g. Generalized Einstein-Aether theories (Zlosnik, Ferreira & Starkman 2007), non-minimally coupled scalar-tensor theories (Bruneton & Esposito-Farese 2007), non-uniform dark fluid theories (Halle, Zhao & Li 2008), Bimetric MOND theories (Milgrom 2010), MOG (Moffat 2006), Entropic gravity by Erik Verlinde, a new ReBEL force acting only between dark matter paticles (Keselman, Nusser & Peebles 2010), and also modified inertia theories (Milgrom 1994, Milgrom 1999, see also Section “What is the meaning of the critical parameter a0” below).

It is important to realise that the need for cold dark matter arises only within the framework of Newtonian dynamics. In MOND and other frameworks none is needed.

As we do not yet know what gravitation really is, and given the success of MOND, it emerges that the evidence for the existence of cosmologically relevant cold dark matter is very weak indeed. The interjection that General Relativity (GR) is extremely well tested is not valid here. GR has only been tested in the Solar System and not in the extremely weak field limit. Furthermore, it is rather obvious that the tests which GR has passed must also be passed by any alternative theory of gravitation. MOND does this through the relativistic estension.

Any gravitational theory needs to account for the observed properties of astronomical phenomena, and so astronomical data test our theories of gravitation and mattter. This is what we are doing in the Stellar Populations and Dynamics Research (SPODYR) group (see Question C.I).

But we are also testing MOND. In fact, one of the hardest tests devised for MOND has been developed by SPODYR (Baumgardt, Grebel & Kroupa 2005) “Using distant globular clusters as a test for gravitational theories“. The test is difficul because high-resolution spectroscopic data are needed for many stars in many very distant faint star clusters – it is the stuff for the largest and most-expensive telescopes on Earth.

Here is a listing of some of the tests performed on MOND by a number of research groups. We return to the star-cluster tests at the end :

1) For example: surface density of normal/baryonic matter dictates where the effect attributed to dark matter appears

Stacy McGaugh (2005, PhRvL)  writes in his abstract:

A fine balance between dark and baryonic mass is observed in spiral galaxies. As the contribution of the baryons to the total rotation velocity increases, the contribution of the dark matter decreases by a compensating amount. This poses a fine-tuning problem for ΛCDM galaxy formation models, and may point to new physics for dark matter particles or even a modification of gravity.


The above figure (klick on it to get a larger version) is Fig.4 from McGaugh (2005). Each pair of open and filled circles lying above or below each other is for one and the same galaxy. The blue open circles show the fraction of the peak rotational velocity of a galaxy which is due to the normal matter in the galaxy, while the black filled dots are the contribution by dark matter in the galaxy (assuming Newtonian dynamics holds true). Note how dark matter magically appears when the normal matter (blue circles) becomes unimportant. 

The above Fig. 4 of this research paper is a completely theory-independent demonstration that in real galaxies there is an extremely fine balance where dark matter is allowed to emerge. Fig.4 shows the relation between the baryon surface density (and hence the typical baryon-induced gravitational acceleration in a given galaxy) and the contribution of  “dark matter” to the rotation curve at its peak-radius.

This correlation is completely unexpected and unexplained in LCDM. But, it is a direct consequence of MOND if MOND is the correct description of the dynamics of galaxies. In a MONDian universe, the dark matter in Fig.4 is phantom dark matter (see below), i.e. unphysical dark matter which a Newtonian observer requires to put into the galaxy in order to explain the observed rotation curve.

Related to to the above, Gentile et al. (2009, Nature) make a perplexing discovery. They write in their abstract

Here we report that the luminous matter surface density is also constant within one scale-length of the dark halo. This means that the gravitational acceleration generated by the luminous component in galaxies is always the same at this radius. Although the total luminous-to-dark matter ratio is not constant, within one halo scale-length it is constant. Our finding can be interpreted as a close correlation between the enclosed surface densities of luminous and dark matter in galaxies.

That is, MOND is more to galaxies than merely their rotation curves: Real galaxies have a disribution of normal, i.e. baryonic, matter which can be observed. It then turns out that somehow, magically, the “dark matter” emerges according to this disribution. In LCDM this simply cannot be and is not the case: in LCDM it is the distribution of dark matter which dictates what is happening through the formation process. Different formation histories and different environments will hence lead to different relative distributions of dark and baryonic matter in different galaxies, meaning that knowing the distribution of normal matter should be an insufficient ingredient to predict the distribution of dark matter.

In real galaxies it is the other way round: normal matter dictates what the gravitational field should do. Only the normal matter is relevant in defining a galaxy. This is essentially a disprove of LCDM, and one may stop considering LCDM further given this observational fact.

2) For example: Rotation curves of disk galaxies

Given the observed distribution of matter in a disk galaxy, its rotation curve can be predicted with great success in MOND. In the vast number of all galaxies these predictions are met with beautiful success (de Blok & McGaugh 1998; Sanders 2010).

Examples can be found on Prof. Stacy McGaugh’s pages:

  1. rotation curves1 (blue dots are observations, red lines are MOND models)
  2. rotation curves2 (blue dots are observations, red lines are MOND models)
  3. comparison  LCDM/MOND
  4. Virtually all galaxies can be fit by MOND, with a few uncertain cases.

The rotation curve fits are obtained for good matches to real stellar mass to light ratia and distances. de Blok & McGaugh (1998) perform a beautiful experiment by showing that any arbitrary, i.e.  even an unphysical, galaxy rotation curve can be fitted by a tailored dark-matter halo. That is, a solution with some dark matter halo can be found. But, only physical, i.e. true galaxies can be described by MOND. This is similar to planetary systems: One can design any kind of planetary orbits (e.g. using wrong force laws) but only the physically correct ones follow Kepler’s laws, namely those where the force law is Newton’s.

As emphasised by Prof. Mordehai Milgrom (2011)in his recent presentation at the Hector Rubinstein Memorial Symposium:

“… all the salient MOND predictions on galactic scales follow as unavoidable, simple, and immediate corollaries of the theory–independent of any messy formation scenario–just as Kepler’s laws, obeyed by all planetary systems, follow from an underlying theory, not from complex formation scenarios. To think, as dark-matter advocates say they do, that the universal MOND regularities exhibited by galaxies will one day be shown to somehow follow from complex formation processes, is, to my mind, a delusion.”

Not purposefully related to MOND, the fact that the majority of galaxies, namely disk galaxies, are found to be simpler than expected, is the same basic tennet (Disney et al. 2008, Nature).

In LCDM a rotation curves cannot be predicted from the observed matter distribution, because of the large variance of CDM halos. For example, Libeskind et al. (2009) analyse an N-body sample of 30946 MW-mass DM host halos with mass in the range 2 × 10^11 Msun to 2 × 10^12 Msun for the properties of their substructure distribution. They first select from this sample only those halos that host a galaxy of similar luminosity as the Milky Way (specifically, galaxies more luminous in the V-band than MV = −20). From this remaining sample of 3201 (10 per cent) hosts, they select those that contain at least 11 luminous satellites, leaving 436 (1.4 per cent) host halos. In this sample of 436 systems, about 30 per cent have 6 luminous satellites with orbital angular momenta aligned to a degree similar to that of the MW system. Thus, only 0.4 per cent of all existing MilkyWay mass CDM halos host a MilkyWay-type galaxy with the right satellite spatial distribution. And, in the Local Group the other major dark halo is that of Andromeda, and Andromeda is quite similar to the MilkyWay. This is consistent with the above Disney et al. (2008) finding, but not with the variance expected in LCDM as documented by Libeskind et al.

This immediately implies that, given an observed disk galaxy’s distribution of normal matter, its rotation velocity cannot be predicted (prior to the actual measurement) in LCDM. With MOND, however, the observed distribution of light in a galaxy allows a precise prediction of the rotation curve, modulo knowledge of the surrounding matter distribution (the “external field effect“).

3) For example: the external field effect

The external field effect plays an important role in MOND. It is related to, but not the same as a tidal field, and is rather complicated. It arises due to the non-linearity of MOND. For example, a galaxy or star cluster which has an internal gravitational field which is very weak and in the MOND limit will appear Newtonian if the external field is sufficiently strong. This means that a star’s motion in such a system will obey Newton’s laws rather than MOND, although MOND is correct.

Famaey et al. (2007) write in their Introduction:

In practice however, no objects are truly isolated in the Universe and this has wider and more subtle implications in MOND than in Newton-Einstein gravity, for the very reason that MOND breaks the Strong Equivalence Principle (SEP).

They show that the local escape speed from the Milky Way is predicted to be 550 km/s with a realistic estimate of the MONDian external field acting on the Milky Way from Large Scale Structure of a0/100… This 550 km/s is precisely what is measured in the solar neighbourhood from a local sample of high velocity stars moving faster than 300 km/s.

Furthermore, isolated warped disk galaxies are difficult to understand in standard gravity, even in the LCDM context, apart from invoking unlikely huge starless CDM halos. But in MOND (Combes & Tiret 2010), the external field, even when it is very weak, induces a differential precession of the galactic disk around its direction, which creates warps even in isolated galaxies.

4) For example: The Milky Way

Of course, not only the local escape speed is compatible with MOND in the Milky Way. As all other disk galaxies, the Miky Way is of course also MONDian.

Famaey & Binney (2005) state in their abstract:

Both microlensing surveys and radio-frequency observations of gas flow imply that the inner Milky Way is completely dominated by baryons, contrary to the predictions of standard cold dark matter (CDM) cosmology. We investigate the predictions of the modified Newtonian dynamics (MOND) formula for the Galaxy given the measured baryon distribution. Satisfactory fits to the observationally determined terminal-velocity curve are obtained for different choices of MOND’s interpolating function.

While McGaugh (2008) writes:

Using the Tuorla-Heidelberg model for the mass distribution of the Milky Way, I determine the rotation curve predicted by MOND (modified Newtonian dynamics). The result is in good agreement with the observed terminal velocities interior to the solar radius and with estimates of the Galaxy’s rotation curve exterior thereto. There are no fit parameters.

Thus, within the closest galaxy we can study, namely our Milky Way, where we have highly resolved observational three-dimensional data, there is absolutely no astronomical evidence for cold dark matter and MOND works.

5) For example: Elliptical galaxies 

That disk galaxies are perfect Milgromian objects is well established by now. This accounts for nearly 80% of all galaxies. But what about the other major class of galaxies, namely elliptical galaxies? These mostly occur in galaxy clusters and are much rarer than disk galaxies. The stars in elliptical galaxies move on chaotic (often boxy) orbits which are all over the place, which is why elliptcal galaxies appear ellitpical, i.e. nearly round (in disk galaxies the stars and gas move on nearly circular orbits about a common center).

So if MOND is the correct dynamical theory for galaxies in general, then it must obviously also hold for elliptical galaxies:

Tiret et al. (2007) studied the predictions for elliptcial galaxies made with Newtonian gravity, either containing pure baryonic matter (i.e. without CDM), or embedded in massive CDM haloes. Tiret et al. also studied the properties of elliptical galaxies in MOND.

The standard CDM model has problems on a small scale (within the central 20kpc), and the Newtonian pure baryonic model has difficulties on a large scale (out to 200 kpc from the galaxies), that is, in LCDM there is no consistently fitting description of elliptical galaxies.

However, with MOND both scales are accounted for naturally.

While MOND thus makes excellent predictions for relatively isolated elliptical galaxies, when these are embedded in a strong external field (see above) the predictions can be slightly different (Wu et al. 2010), but no observations have ruled out these small predicted effects.

In a very recent research paper Richtler et al. (2011) study the apparent dark matter halos of ellitpical galaxies.

The authors conclude that the benchmark scaling relations that have been found for dark halos of ellipticals, especially on the central DM phase-space density and volume density as a function of the galaxy’s baryonic mass, are remarkably similar to the scaling relations of the predicted phantom halos of MOND.

What are “phantom dark matter halos”?

Perform the following Gedanken experiment: Assume you live in a MONDian universe, but you think you live in a Newtonian universe.

When you observe an elliptical galaxy (or any kind of galaxy), you will see that the matter in the galaxies moves differently than it ought to. Since you are convinced that you live in a Newtonian world, you have no option but to explain the strange motions through the presence of additional unseen matter, i.e. dark matter. It must be cold dark matter (i.e. massive particles that cannot travel at relativistic speeds), because hot dark matter (made of particles moving near the speed of light) cannot cluster on galaxy scales. You can then calculate the distribution of the cold dark matter from the strange motions.

But in truth the strange motions are only strange to an observer who thinks he/she lives in a Newtonian world. In actuality, he motions are perfectly correct in the real MONDian universe, in which there is no dark matter.

So the Newtonian observer deduces cold dark matter, but it is phantom dark matter because it has no physical reality and is only needed to explain the motions of stars and gas in a MONDian universe for someone who interprets the motions using Newtonian dynamics.

The conclusion of Richtler et al is that

whatever the true physical reason for the strange motions, it is remarkable that a recipe (MOND), which is known to fit rotation curves of spiral galaxies with remarkable accuracy, also apparently predicts the observed distribution of “dark matter” in elliptical galaxies.

6) For example: Tully-Fisher law  and  Faber-Jackson relation

While MOND thus works amazingly well to reproduce the details of the dynamics of individual galaxies, it also sheds light on very general scaling relations that are difficult to understand otherwise.

The Tully-Fisher law (which all known rotationally supported galaxies obey) comes out precisely in MOND (Sanders & McGaugh 2002, ARAA). And, the Faber-Jackson relation (which all known elliptical galaxies obey) also comes out in MOND precisely (Sanders 2010). There is no natural (i.e. plausible) path to any of these observed relationships in LCDM.

But, the Tully-Fisher data depend, for individual normal disk galaxies, largely on the mass of the galaxy which is in stars. For example, our Galaxy’s disk is made up to about 85% of stars, and only about 15% of it is in gas and dust. MOND-critics would claim that the excellent MOND-fit to the observed data depends on this mass which is, however, claimed to be uncertain.

Stacy McGaugh (2011) has just very recently concentrated on testing MOND and LCDM for disk galaxies in which most of the mass is in gas. The gas distribution in the galaxy can be measrued well with radio telescopes, and with the most recent deep surveys excellent data are now available for such low-surface brightness galaxies (they are faint because their  baryonic mass is mostly in gas rahter than stars).

In his abstract:

Here I report a test using gas rich galaxies for which both axes of the BTFR can be measured independently of the theories being tested and without the systematic uncertainty in stellar mass that affects the same test with star dominated spirals. The data fall precisely where predicted a priori by the modified Newtonian dynamics (MOND). The scatter in the BTFR is attributable entirely to observational uncertainty. This is consistent with the action of a single effective force law but poses a serious fine-tuning problem for LCDM.

In the paper he writes

The specific BTFR that the data follow is unique to MOND. Indeed, to the best of my knowledge, MOND is the only theory to make a strong a priori prediction for the BTFR. The dark matter paradigm makes no comparably iron-clad prediction.


In order to reconcile LCDM with the data, we must invoke additional parameters.


Reproducing the observed BTFR in LCDM requires a remarkable degree of fine-tuning.

This research paper caused major interest in the press:

Science has written a story about it:  More Evidence Against Dark Matter?

BBC also: Dark matter theory challenged by gassy galaxies result

and Science Daily: Gas Rich Galaxies Confirm Predictions of Modified Gravity Theory  

and Nature: Alternate theory poses dark matter challenge

and The Weizmann Institue of Science also: Dark Matter: A rruling Theory with no Clothes?

The Weizmann Site contains a vigorous and partially very aggressive discussion started by commentators who objected its contents. This discussion gives an insight as to the current scientific atmosphere in which gravitational research needs to be conducted.

7) For example: Tidal Dwarf Galaxies (TDGs) are MONDian


Sensational movie of a galaxy collision calculated using a MONDian integrator by Tiret & Combes (2008), from the TDGBonn 2009 conference website. Klick on the movie and a new page appears. Then download the movie or klick on “tiret-mond1.m4v”. This movie is sensational because it showsfor the first time how galaxies collide in MOND without any dark matter, and how tidal dwarf galaxies form naturally in MOND. 

When galaxies interact they expell matter in the form of tidal tails. In the tidal tails the gas and perhaps some stars may collapse locally to make star clusters or dwarf galaxies. The above movie is a major break through achieved by Oliver Tiret and Francoise Combes as it is one of the very first ever computations, in a MONDian universe, of two colliding galaxies. This calculation is done without cold dark matter! One can nicely see how the tidal tails develop, and how later-on small regions of them collapse to make bound objects of dwarf galaxy mass. In this simulation about 4 or more tidal-dwarf galaxies (TDGs) form, but probably many more would form if a computation with higher-resolution could be done. Thus, the formation of TDGs is natural in MOND, and they would arrange themselves around their host galaxy naturally in a Disk of Satellites, as is in fact seen for the Milky Way (see point 4 in Question CI).

The TDGs cannot have cold dark mater, because the CDM particles cannot be captured in significant quantities by these small objects. But, TDGs which cannot have dark matter in the LCDM model, are observed to have CDM! This is a massive failure of the LCDM model.

TDGs however show a behaviour just as expected in MOND – they are excellently described by MOND. Infact, the prediction of MOND is verified, since the rotation curves of TDGs have been observed only recently decades after MOND was invented:

The TDGs follow the Tully-Fisher law (Gentile et al. 2007, A&A). How is this possible? If LCDM were right, then disk galaxies (which would be in a dark-matter halo which defines the rotation curve) would form a sequence in the rotation speed vs luminosity diagramme. But, TDGs would not be in dark matter halos (Barnes & Hernquist 1992, Nature) and so would not be able to lie on the same sequence. But they do!!

Thus TDGs and normal disk galaxies must be defined by an underlying theory which has nothing to do with dark matter. MOND is precisely such a theory. And indeed, assuming MOND is right, then TDGs as well as normal disk galaxies must lie on the same sequence, as is observed.

This latter point is extremely important, and we need more cases (three TDGs have been observed so far, but telescope time has not been granted to observe more despite quite a few proposals being handed in).

8) For example: Milky Way satellite galaxies are MONDian

The Milky Way has about two dozen dwarf-spheroidal (dSph) satellite galaxies. These are similar but fainter than dE galaxies that are found mostly in galaxy clusters. While the spatial arrangement of the dSph satellites about the Milky Way is not reconciable with the LCDM model (see above), they do appear, to a standard-cosmological (i.e. Newtonian) observer, to be heavily dominated by dark matter.  The normal matter (the stars – these little satellites contain virtually no gas) makes only 1/10th to 1/1000th of the total (CDM+stars) mass of the objects. This comes about if the motions of the stars are interpreted by assuming Newtonian dynamics to be valid.

If MOND were the correct dynamical framework, would a consistent description of the dSh satellites be possible? Consistent means here that their internal properties (see above) and their spatial arrangement would need to make sense.

In the LCDM framework a consistent description fails because their spatial arrangement and their internal properties are not explainable consistently (see Question CI). In LCDM, their spatial arrangement and motion about the Milky Way imply them to be ancient TDGs, but then they cannot have dark matter. If they are taken to be the dark-matter dominated sub-structures expected to be present in the standard model, then their spatial arrangement about the Milky Way cannot be explained, and their internal properties also not.

A number of researchers have studied the Milky Way satellite galaxies in MOND and MOG:

Angus (2008, MNRAS) (“Dwarf spheroidals in MOND“) demonstrates that most of the dSph satellites he studied have normal stellar populations without needing any dark matter, if the satellite masses are computed using MOND.

Hernandez et al (2010, A&A) (“Understanding local Dwarf Spheroidals and their scaling relations under MOdified Newtonian Dynamics“) noticed an interesting correlation between the mass-to-light (M/L) ratios of local dSphs (under MOND or DM), and the ages of their younger stellar populations, in the sense that M/L ratios are clearly smaller for the dwarfs with the younger stars. This is of course naturall in any non-DM scenario, but a contrived coincidence under DM. 

Mendoza et al. (2010, MNRAS) (“A natural approach to extended Newtonian gravity: tests and predictions across astrophysical scales“) investigate mass-velocity scalings of all self-gravitating systems in non-Newtonian frameworks, finding a generally excellent and natural (without needing ad-hoc assumptions) understanding of the observed scaling relations.

McGaugh & Wolf (2010, ApJ) (“Local Group Dwarf Spheroidals: Correlated Deviations from the Baryonic Tully-Fisher Relation“) perform an impressive and comprehensive study of the dSph satellites. They discover remarkable regularities in the data, but only within the MOND famework. LCDM leads to no understanding of these systems: one sees noise and no physics. In MOND however, beautiful correlations emerge which nicely show what intuition would expect in any case, namely the susceptibility of the purely stellar satellite dwarf galaxies to tidal disruption in dependence of their (purely stellar) mass and orbital properties.

9) For example: Galaxy clusters, the CMB and hot dark matter

As argued by Prof. Robert Sanders (2007, MNRAS), for galaxy clusters there is a mild missing mass problem in MOND, but only at the level of a factor of 2-3. This may easily be accounted for by additional baryons (as suggested by Milgrom 2011;  see also Section “Does MOND still need dark matter?” below). Hot dark matter in the form of 11eV sterile neutrinos would also be a viable and a consistent solution, as computed by Angus, Famaey & Diaferio (2010, MNRAS). The WMAP power spectrum is then also explained very accurately with the same 11eV hot dark matter with a similar cosmological expansion history as LCDM but outperforms LCDM on galaxy scales (Angus 2009, MNRAS)!

Sterile neutrinos are a plausible extension of the standard model of particle physics which could help solving many observed anomalies (see e.g. p. 187 of Strumia & Vissani), and which, as stated in Giunti & Li (2009), “may be heralds of alternative cosmological models”… However, they suffer from one of the important problems of CDM: there is no experimental evidence for them.


Fig. 1 from Angus (2009): “This shows the data of the CMB as measured by the WMAP satellite year five data release (filled circles, Dunkley et al. 2008) and the ACBAR 2008 (Reichardt et al. 2008) data release (triangles). The lines are the LCDM max likelihood (dashed) and the solid line is the fit with an 11eV sterile neutrino” (hot dark matter). Here you can find and share the MOND WORKS poster.

10) For example: distant star clusters

As stated above, one of the hardest tests devised for MOND has been developed by SPODYR (Baumgardt, Grebel & Kroupa 2005) “Using distant globular clustersasa test for gravitational theories“. The test is difficult because high-resolution spectroscopic data are needed for many stars in many very distant (further from the Milky Way than 20kpc) faint star clusters – it is the stuff for the largest telescope on Earth.

MOND is the dynamical model for galaxies. Star clusters probe a different mass and length scale, and because MOND only has an acceleration scale it must be valid on star-cluster scales as well.

The idea here is to seek and observe such star clusters that have an internal (i.e. given by its own stars) and an external (given by the MilkyWay) gravitational acceleration which is below the MOND limit. By observing the motions of stars in such star clusters one can find out if they follow Newton’s laws or MOND.  The motions of the stars need to be analysed statistically from spectroscopic (blue- or red-shift) observations because we can only get current snap-shots, given that the star orbits through a cluster in about Myr.

A list of star clusters suitable for this test has been identified in the above Baumgardt et al. research paper. Subsequently, expensive telescope time has been won and star cluster Pal 14 (distance from Milky Way: 69kpc) was observed (Jordi et al. 2009). The observations suggest MOND may be excluded on star-cluster scales.

But, this exclusion would only be the case if the cluster is on a circular orbit about the Milky Way. And, subsequent work has shown that the exclusion is not statistically significant (Gentile et al. 2010). This is verified with numerical MOND simulations by Haghi, Baumgardt & Kroupa (2011). The line-of-sight velocities of many more stars are required to allow a statistically significant test of MOND.

Similarly, Baumgardt et al. (2009) measure and Sollima & Nipoti (2010) compute the motions of stars in distant star clusters in MOND and find “A comparison with recent spectroscopic data obtained for NGC2419 suggests that the kinematics of this cluster might be hard to explain in MOND.”

Therefore, currently the evidence is against MOND on the scales of star clusters. However, this evidence is not yet conclusive because MOND is non-linear leading to effects which are not intuitive. As PK suggested some years ago (see Haghi et al. 2011) a cluster on a radial orbit about the Milky Way may transcend from the Newtonian regime to the MONDian regime faster than the stellar motions within the cluster can adap. The cluster may look Newtonian even though it is in the MOND acceleration regime. Whether this is a viable scenario for the Milky Way star clusters observed to date needs to be shown through explicit dynamical modelling.

As another test of gravitation, Scarpa & Falomo (2010, and references therein) analyse the motions of cluster stars near the massive globular cluster omega Centauri:

We conclude that there are strong similarities between globular clusters and elliptical galaxies, for in both classes of objects the velocity dispersion tends to remain constant at large radii. In the case of galaxies, this is ascribed to the existence of a massive halo of dark matter, which is physically unlikely in the case of globular clusters. This similarity, if confirmed, is best explained by a breakdown of Newtonian dynamics below a critical acceleration.

Another alternative: Modified Gravity (MOG)

Of the various other developments mentioned near the top, MOG has been most widely applied to galactic problems. Prof. Dr. John W. Moffat at the Perimeter Insitute for Theoretical Physics, Waterloo, Canada, began thinking about an alternative gravity model (MOG) because he was curious about how robust the standard CDM paradigm was regarding the fitting of data (Moffat 2011, private communication). He modifed GR by incorporating additional fields which effectively lead to a scale-dependend strength of gravity which assumes a Yukawa-type behaviour in the week-field limit.  With the current version of MOG, galaxy rotation curves and galaxy clusters as well as a cosmological model can be explained without the need for any dark matter, although the three running parameters need to be fixed through observational data at each relevant scale (globular clusters, disk galaxies, galaxy clusters, cosmology).

Some of the recent research papers on MOG:

Moffat (2011): “Modified Gravity or Dark Matter?”

Toth (2010): “Cosmological consequences of Modified Gravity (MOG)”

Moffat & Toth (2009): “Fundamental parameter-free solutions in modified gravity”. Quoting their abstract:

Modified gravity (MOG) has been used successfully to explain the rotation curves of galaxies, the motion of galaxy clusters, the bullet cluster and cosmological observations without the use of dark matter or Einstein’s cosmological constant. We now have the ability to demonstrate how these solutions can be obtained directly from the action principle, without resorting to the use of fitted parameters or empirical formulae. We obtain numerical solutions to the theory’s field equations that are exact in the sense that no terms are omitted, in two important cases: the spherically symmetric, static vacuum solution and the cosmological case of a homogeneous, isotropic universe. We compare these results to selected astrophysical and cosmological observations.

Moffat & Toth (2008) point out that distant star clusters are predicted to be Newtonian if MOG were correct. If it turns out that the star-cluster test of MOND described above fails (i.e. if we discover that the star clusters are systematically Newtonian having a small velocity dispersion), then we would have the situation that MOG, which captures MOND behaviour on galaxy scales, would have been verified over MOND or that MOND woud need a length-or mass-scale-dependent acceleration scale (returning to LCDM is out of the question – see Question C.I). The abstract of Moffat & Toth (2008):

Globular clusters (GCs) in the Milky Way have characteristic velocity dispersions that are consistent with the predictions of Newtonian gravity, and may be at odds with Modified Newtonian Dynamics (MOND). We discuss a modified gravity (MOG) theory that successfully predicts galaxy rotation curves, galaxy cluster masses and velocity dispersions, lensing, and cosmological observations, yet produces predictions consistent with Newtonian theory for smaller systems, such as GCs. MOG produces velocity dispersion predictions for GCs that are independent of the distance from the Galactic center, which may not be the case for MOND. New observations of distant GCs may produce strong criteria that can be used to distinguish between competing gravitational theories.

What is the meaning of Milgrom’s a0?

Before proceeding we need to note from observations that in all stellar systems, whenever the force from gravity falls below a critical acceleration a0, we see that the stars or gas move differently than they should. This is very nicely demonstrated by Prof. Stacy McGaugh’s recent research paper, as well as by many other research papers already published.

It is as if a resistance to the motion disappears. And this behaviour is perfectly calculated by the MOND formula which Milgrom discovered in about 1983. This change in motion happens at such a weak gravity that we cannot reach it in our Solar System, not even in the vicinity of the Sun, where our Galaxy is exerting too strong a pull.

The usuall interpretation of this deviation from Newtonian motions is through the appearance of cold dark matter (CDM). This CDM would have to behave differently in different galaxies to account for the observations, which the theory of CDM does not allow though. Unless of course additional “dark forces” are introduced.

In this sense CDM is similar to phlogiston, which had been postulated  to be a substance related to burning phenomena. But in order to account for different phenoma phlogiston had to have incompatible properties and it was discarded as a viable physical entity even before the advent of modern chemistry and quantum mechanics.

Returning to MOND, what does this critical very weak force (or technically critical acceleration, a0) mean? It is quite clear that this new constant a0 (call it Milgrom’s constant) is truly new physics at a fundamental level which is not understood yeat but which is at the very heart of the issue of the origin of mass (Higgs boson), space and time. Theoretical physicists have, so far, not arrived at a good description or theory of these problems.

Here is a citation from Wikipedia’s MOND entry: where we read:

To explain the meaning of this constant, Milgrom said : “… It is roughly the acceleration that will take an object from rest to the speed of light in the lifetime of the universe. It is also of the order of the recently discovered acceleration of the universe.”

Milgrom’s constant thus appears to be related to thel arge-scale propeties of the universe.

Another way of looking at a possible deeper physical meaning of MOND is at the very centre of modern physics:

What is inertial mass? What is gravitational mass? And, why should they be equal?

Inertial mass: If you push any object in free space you will feel a resistance. The heavier the object is, the more resistance you will feel. Thus, there is inertia to a change of motion.

Gravitating mass: The same object also curves space-time around it, i.e. it exerts a gravitational pull on other objects.

One of the major postulates of modern physics is to insist that inertial and graviating mass are equal, that they are equivalent:

inertial mass = gravitating mas

(this is known as the Equivalence Principle and is at the heart of General Relativity).

One way of looking at MOND is as follows:

When the gravitational field becomes extremely weak, inertial mass and gravitational mass may not be equal any longer and the above equivalence may be broken. If this were to be the case, then this would revolutionise physics at a most fundamental level.

How can this come about and how does MOND enter? Again, Milgrom has a suggestion which is summarized in the appendix of this paper by Kroupa et al.:

Take an apple in completely empty flat space and push it. As it it accelerates it begins to “see” the vacuum in front of it getting hotter (the energy fluctuations in front of it get blue shifted). The resulting radiation pressure exerts a force against the ball (Unruh radiation) and may be related to what we feel as the inertial mass.

The same apple, if it is in curved space time and pushed it will additionally “see” a radiation field which comes from the cosmological horizon (the Gibbons & Hawking radiation). This radiation is essentially the same radiation you would observe coming from a black hole as the energy vacuum fluctuations at its event horizon get split into a part that ends up in the hole and a part that is left in our universe. That is, we can think of our universe as being the inside of a black hole.

When the push on the ball is extremely weak the Unruh and the Gibbons & Hawking radiation may cancel, such that pushing the apple gets easier. The resitance weakens.  The apple can then move faster more rapidly, and this is exactly what we see in those regions of all stellar systems where the gravitational pull is very weak.

That is, MOND emerges from the quantum mechanics of the vacuum plus the whole universe. Milgrom was able to derive the MOND transition function from this concept. This is why MOND is so amasingly exciting. But, the above is merely a proposition, and it is not clear at this stage whether Unruh radiation exists.

Milgrom’s discovery of a0 is likely as epochal as Planck’s discovery of h.  When Planck introduced h as a “Hilfsgroesse” (German for auxilliary number) he had no idea what it meant. It’s relation to energy quantisation was discovered much later. Likewise, the meaning of a0 is not completely clear yet.

It is evident though that by following the path indicated by MOND we are likely to come closer to a quantum formulation of gravity thereby quite certainly completely revolutionizing our understanding of gravity because the equivalence between inertial and gravitating mass is at the very heart of the whole formulation of General Relativity:

It is not at all certain that the formulation of gravity as being the consequence of the curvature of space-time would even hold anymore if this interpretation of MOND is the right one, even though this description of gravity by Einstein would have proven to be an amazingly powerful approximation in the regime of strong gravity, on Earth, in the Solar System (otherwise GPS wouldn’t work), for binary pulsars, etc.

Does MOND still need dark matter?

. . . and does that mean that dark matter exists whatever happens?

Well, yes, “dark matter” certainly exists!  But it depends on what you call dark matter:

It is well known that there are missing baryons. In fact, after the Big Bang about 60% of all normal matter “disappeared”.  Astronomers do not know where this matter is. It might be hiding as dark clumps of cold gas (Pfenniger, Combes & Martinet 1994), and it would then have the dynamical properties of cold dark matter. Also, there are burned-out stars, neutron stars and black holes, which can, for example, dominate the dynamics of the central region of old star clusters.

So we know that we do not see all of the normal matter (yet),  and one may call it dark matter if one likes to do so.

It is very possible that MOND only needs this kind of  “dark matter”! (but see point 9 above: “For example: Galaxy clusters  and  hot dark matter”).

While it is true that some relativistic extensions of MOND need other forms of it (e.g. hot dark matter or dipolar dark matter), none needs CDM! 

That is, searching for cosmologically-relevant WIMPS would be a waste of time if the real universe is MONDian. 

Axions or axion-like particles, on the other hand, would be relevant only if their mass is varying and as such they break the weak and strong equivalence principles. They thus induce modified gravity effects, thereby perhaps opening a path to explain MOND (Fuzfa & Alimi 2010). But plain CDM axions would be as useless as WIMPS.

Concluding Remarks:

The many attempts to bring LCDM into agreement with reality on scales of about 10Mpc and less have failed (see Question CI). MOND, as discovered by Milgrom in 1983, is the currently best theory for classical, i.e. non-relativistic, dynamics. Without fine-tuning it describes what we observe to a most excellent degree of accuracy.  It accounts for observed astronomical data ranging from dwarf galaxies to massive galaxy clusters and is in excellent agreement with the Cosmic Microwave Background. It reduces significantly the need for dark matter on large scales, and needs no introduction of cold dark matter on small scales. The tremendous success of MOND to account for observed reality compared to the failures of LCDM is nicely summarised by Stacy McGaugh in this table.

The hard reality which many researchers and politicians will have to face is that the success of MOND implies that the expensive searches for cosmologically relevant cold dark matter particles (WIMPS, axions) are futile. There is no reasonable astronomical evidence for cosmologically relevant cold dark matter particles.

The possible addition of some hot dark matter to account for lensing and the CMB makes a fully consistent picture, also with the standard model of particle physics, and is not a problem for MOND. But, since about 60% of all baryons has gone missing since the Big Bang, it is natural that some dark baryonic matter must play a role in galaxy clusters.

Finally, the work on these and other alternatives has demonstrated above all else that the LCDM model is not unique.

25. Question C.I: What are the three best reasons for the failure of the LCDM model? I: Incompatibility with observations


The development of the concordance cosmological model (CCM) over the past 40 years is based on the addition of at least three unknown (“dark”) physical phenomena (inflation, cold dark matter, dark energy), in an attempt to make Einstein’s field equation account for the distribution of matter on galactic and larger scales. None of these are understood nor experimentaly verified today. While these may constitute true discoveries of new physics, much as in the spirit of the past when for example Neptune and the neutrino were postulated to exist based on not understood observations, these dark additions also have a parallel in the Ptolomaic model which is based on a series of complex additions to circular motions in order to provide a calculation tool for the Solar System prior to the discovery of Kepler’s and later Newton’s laws. On close scrutiny the latter analogy appears to be the favourable one because the CCM is not able to account for the observed distribution of matter on scales of 10Mpc and less, where a massive computational effort by many groups has been able to quantify the theoretical distribution of matter. Meanwhile, new dynamical laws have been discovered which are extremely successful in accounting for the appearance and motion of matter on galactic scales and above. At the same time, it is emerging that the CCM is not unique in accounting for the large-scale matter distribution nor for Big Bang Nucleosynthesis nor for the cosmic microwave radiation. This suggests rather unambiguosly that our understanding of gravity is not complete. This conclusion, obtained purely from astronomical data, is nothing else but the statement that we do not have a good physical theory of matter, mass, space and time nor do we  know how and if they can be unified. 


As introduced in the previous contribution to The Dark Matter Crisis, Question A: Galaxies do not work in LCDM, sociology and majority views, PK was recently contacted by a few people, and here are excerpts from some of the questions asked and the replies. These help to illustrate some of the issues at hand. The questions are

A) So the LCDM model fails on scales smaller than about 8 Mpc?

B1) What is a galaxy?

B2) What is a galaxy? (Addendum on the relaxation time)

C) What are the three best reasons for the failure of the LCDM model?

I: Incompatibility with observations (this contribution)

II: MOND works far too well !

III: Fundamental theoretical problems

D) What about the Bullet cluster?  And what about the Train-Wreck cluster Abell 520?

E) Why is the main stream community so reluctant to  go along with accepting the failure of LCDM?

This contribution deals with Question C, which may be taken to be central to The Dark Matter Crisis, while upcoming contributions will concentrate on the remaining questions.

The three best reasons for the failure of the LCDM model: 

They can be summarised in three categories. Here is category I. Categories II and III can be found in seperate contributions as outlined above.

I) Incompatibility with observations:

Failure upon failure requires multiple dark additions:

The logical framework we are discussing (see also The standard model of cosmology) rests on assuming Einstein’s General Theory of Relativity(GR) to be a true description of the interconnection of matter, mass-energy and gravity. This is indeed a very well motivated assumption, because experiments in laboratories have confirmed that on earth GR is valid to extremely high precision. But also peculiarities about the orbits of Mercury (perihel shift) or pulsars are very well explained with GR.

However, this assumption fails when galaxies or the universe as a whole are considered, unless new, unknown physics is postulated to be dominant on this scale.

Assuming GR to be valid implies that the universe begins in a highly compact state. However, the Universe is observed to be flat already “at the next instant” after the Big Bang. Also, every part of the universe we know has the same physics, and so must have been in causal contact which is impossible if the universe expanded similarly as is seen today.

So inflation (I) is introduced (leading to the GR+I model) as a mathematical trick to inflate the universe by a factor of at least 10^78 in volume in an incredibly short time (about 10^-32 seconds) such that all parts in the observable universe were in causal contact before inflation and such that it is flat by the time it can be observed for the first time (the cosmic background radiation field). But then structure formation still does not work, because the structures (large-scale filaments, galaxy clusters, elliptical galaxies) are observed to evolve too rapidly with time; they appear too early after the Big Bang.

Cold dark matter (CDM) is introduced which helps the structures to grow in the GR+I+CDM model, and it needs to be cold or at best warm to account for the growth of structures. The idea here is that this hypothetical matter does not interact with photons and so can decouple and begin to re-arrange itself gravitationally long before the normal (baryonic) matter decouples from the photons.  The dark matter particles must be moving slowly after the Big Bang, that is, they must have a large mass (e.g. WIMPs), as otherwise they would not be able to clump through gravity to make the seed dark matter halos within which the later galaxies emerge in the model. Hot dark matter would be constituted by light particles that can move at a speed close to that of light and they would not be able to clump to make the halo seeds, in this  GR+I+dark matter model.

In the GR+I+CDM model the seed halos accrete more dark matter and other seed halos. The waxing dark matter halos are able to accrete normal matter, which is cooling as a result of cosmic expansion. From this normal matter stars form making the first galaxies.

Note that the model requires that there is about five times more dark matter than normal matter, and we emphasize that a candidate for a DM-particle has not been found in a laboratory so far. Its existence thus remains speculation at the present.

But, even this GR+I+CDM model, which already relies on most of the universe being made up of unknown ingredients (I+CDM) still does not fit the data: By studying distant standard-candle explosions (supernovae of type Ia) it has been found that the universe is today already larger than it ought to be. In fact, its expansion seems to be accelerating. This can be obtained in the GR+I+CDM model only by introducing another field similar to inflation (I) but which is just now becoming active or important thereby ripping the universe apart at an ever increasing rate. This is described mathematically in the equations by the cosmological constant Lambda, and is also referred often to as a dark energy (DE), such that the currently complete standard model becomes the GR+I+CDM+DE=LCDM model. In this model, which is described by about 14 parameters, the universe consists of 95% dark unknown stuff (dark matter plus dark energy, next to inflation).

This DE is a constant energy density, that is, every cubic centimeter contains the same amount of DE. Because the Universe expands (in fact at an ever increasing rate), DE increases (at an increasing rate). Thus, energy is not conserved in this model, while energy conservation is usually considered a fundamental principle in physics. One can postulate that this is OK, since the universe may not be an isolated system, and in any case, energy conservation in GR is a difficult problem. But this is equivalent to postulating an unkown “(dark) outside (DO)” (perhaps in higher dimensions) to solve the energy crisis (implying that the LCDM model would be GR+I+CDM+DE+DO). Prof. John A. Peackock writes at the end of section 1.5 of his book on “Cosmological Physics” (1999, Cambridge University Press):

In effect the vacuum acts as a reservoir of unlimited energy, which can supply as much as is required to inflate a given region to any required size at constant energy density.

Assuming this GR+I+CDM+DE+DO model to be valid (the DO assumption linked to energy non-conservation is usually never mentioned) , one can compute how the universe evolves (see Precision Cosmology below). Large research groups in many places (e.g. Potsdam, Heidelberg, Munich, Zurich, Durham, Swinburne) are doing just this. The computations are relatively straight-forward, because they are Newtonian, that is, GR need not be used. The only real complication comes in through the star-formation and gas physics which happen on very small scales of less than a pc. While the claim by the cosmological community is that star formation is a badly understood process, observations of star formation in the Milky Way and nearby galaxies actually give us a pretty good knowledge of what happens when gas turns into stars.

Some cosmologists would therefore erroneously state that the “stuff” that happens on galaxy scales is not more than gastrophysics, that is, not more than weather or just messy cooking, such that the whole model cannot be tested using observations of galaxies.

But, this is wrong, because a vast industry of computational cosmologists has been able to study the formation and evolution of galaxies, even down to satellite galaxies, well, even down to earth-mass dark-matter halos with a size of the Solar System that might be interacing wirth our Solar System (Diemand, Moore & Stadel 2005, Nature):

“We expect over 1015 to survive within the Galactic halo, with one passing through the Solar System every few thousand years”.

Statements on the galaxy-content of each of the dark matter halos are possible because whatever the small-scale baryonic physics does, it is nevertheless subject to conservation laws (conservation of energy and angular momentum), such that the galaxy-sized structures that emerge in the computer must obey these. And, as stated above, we do have good information on star formation.

Explicit tests:

It is therefore clear that in comparing the standard (=LCDM) model on scales of galaxies with the real universe,  we do not check if some gas cloud or star is at a particular position. What one does instead is to test the overall, generic properties of the systems under study. For example, we might wonder how many galaxies are rotating thin disk or spiral galaxies, or, how many galaxies are ellipticals without much rotation, or, how many satellite galaxies does a typical galaxy of some brightness have? Or, how are galaxies distributed in a region of space about 10 Mpc large?

The many parameters that define the GR+I+CDM+DE model have been measured precisely by now such that currently we live in the age of Precision Cosmology. These measurements come from the cosmic background radiation field and the observed distribution of matter on large scales. Simon White presents such evidence at the Dark Matter Debate. LCDM is thus extremely well constrained, that is, there is not much room left for changes in its parameters, assuming of course that the observations and the data analysis has been done correctly. So, within the precisely constrained LCDM model, one can now use super-computers to calculate how matter arranges itself on various scales. For example, one can calculate (the cosmologists often say “predict” although this is not a correct usage of the word) how dark matter halos are distributed in the sheets and filaments, and how structures such as the Local Volume (about 10 Mpc across) or the Local Group of Galaxies (about 1.5 Mpc across) appear in the model.

(NB: the word “predict” is nowadays usually used by cosmologists to mean “calculated” – the true meaning  of “predict” is, however, to quantify some phenomenon before it is observed. Thus, Tidal Dwarf Galaxies (TDGs) are predicted in MOND to lie on the Tully-Fisher relation before the observations verifed this to be the case. In LCDM TDGs cannot be on the Tully-Fisher relation if the Tully-Fisher law is defined by the dark-matter dominated “normal” disk galaxies.)

A truly massive effort documented in countless papers

(for example, arXiv:1101.0816, arXiv:0905.1696, arXiv:0711.2429, astro-ph/0501333, astro-ph/0502496, astro-ph/0503400 all argue that the satellite galaxies can be explained within LCDM)

has been going on for more than ten years to calculate how galaxies emerge and evolve, and how their satellite galaxies are distributed. Clearly this massive effort proves that it is in fact possible to calculate the appearance of structures on galactic scales in the LCDM model.

Today it is clear that this GR+I+CDM+DE model makes precise predictions as to what the generic properties of galaxies are and how they are distributed on scales of 10 Mpc and less. Most if not all of the papers conclude that the particular problem they are approaching can be solved in LCDM, while usually other issues are neglected (e.g. many of the papers deal with the spatial distribution and the number of the satellite galaxies, but ignore their disk-like arrangement about the Milky Way; or they invoke various star-formation and energy-feedback algorithms to attempt to solve the missing satellite problem but then the resulting model is not checked for consistency with galaxies in the Local Void – see below).

The overall portrayal of the status of LCDM by the members of the community involved in this work is then that the LCDM model is quite fine. LCDM is so successful on large scales, that problems on smaller scales tend to be seen as not being major.  This is somewhat surprising, since these issues arise from the best observational data that we have. This is the data on the Local Group and the Local Volume, i.e. data on objects in our cosmic neighborhood.

Concerning the accuracy of the LCDM-model, it is important to understand that a good description of data by a model does not prove that the model is correct. A model or theory can in fact always only be tested and (possibly) falsified, but can never be proven as a matter of principle.

And, by demonstrating that a mathematical model fits on certain scales does not mean that there may not be very different models that also fit just as well.

A historical case in point is the Geocentric or Ptolomaic model: it survived for millenia because it fit the overall world view (We are The Center and there was a Creation Event) and because it was able to account for the observations well, even though it needed to be enhanced through the addition of epicycles and other mathematical artefacts: “It was accepted for over a millennium as the correct cosmological model by European and Islamic astronomers.” The Geocentric (or more correctly the Ptolomaic) model is a good albeit complicated calculation tool for the Solar System (you could still use it today), with which rather precise predictions are possible concerning the positions of the planets and occultations. But, as we know today, it is an unphysical model, and it was ultimately rejected because of modern data (after 1600’s) from beyond the Solar System as well as Galileo’s observations (and it is well known how difficult if not impossible it was for Galileo to convince his peers of what his telescope was showing).

Given the present fact that the LCDM model fits well on large scales, that it is a useful calculation tool, and given the deep implications for our understanding of cosmology and fundamental physics which go along with it, if it were physical (rather than just a mathematical tool), it is important to test the LCDM model. This is similar to back in Galileo’s times: To check on the claims of the dominant viewpoint (perfect celestial bodies moving around the Earth) anyone could build a telescope and test the Ptolomaic model. For example, if the Sun has spots it is not perfect, or if stars show parallax then the Earth moves about the Sun!

We have been performing tests of the LCDM model by taking the observational data and the model calculations published until 2010 by many groups (e.g. those mentioned as astro-ph contributions above). The results of these tests are published in Kroupa et al. 2010. It turns out that LCDM fails on every test performed.  For completeness it ought to be mentioned that we are also testing the leading alternative MOND.

1) For example:  Too many dark-matter-dominted satellite galaxies expected


Local DM density from Via Lactea 2 simulation showing thousands of subhalos. (Source: Diemand et al. 2008).

Structures grow hierarchically.  That is, larger dark-matter structures arise from the collisions of smaller ones. The smaller dark-matter structures do not dissolve typically, but orbit about the emerging large dark-matter halo. Each dark-matter halo is thus full of thousands of dark-matter satellite halos. If each satellite halo would be able to host star formation then our Milky Way, Andromeda and other similar galaxies would have many thousands of satelltie galaxies. But only two-dozen have been found.  This missing satellite problem is an old problem (Klypin et al. 1999; Moore et al. 1999), having arisen as soon as computers became powerfull enough to do CDM calculations with higher resolution.

To solve it, most of the satellite dark halos must somehow be forbidden to make stars. This problem is not fully solved, as is disussed in our research paper, but cosmologists would argue that they are well aware of the problem and it is not new. Many groups claim to have solved it, although they argue amongst each other which of the many proposed solutions is the correct one, some of them being mutually exclusive (e.g. Kazantzidis et al. 2004Kravtsov et al.2004; Tollerud et al. 2008; Koposov et al. 2009).

And, given  the stochastic nature of the merging processes, the number of bright dark-matter dominated satellite galaxies calculated in LCDM to be around each major galaxy such as the Milky Way can vary: some dark matter host halo may acquire a few more than another one.

2) For example:  Tidal Dwarf Galaxies (TDGs)


The Tadpole galaxy showing the formation of new dwarf galaxies along its tidal tail. Image credit: NASA, the ACS Science Team and ESA

Structures grow hierarchically. That is, larger structures arise from the collisions of smaller ones. In such collisions between disk galaxies with gas, new dwarf galaxies can be born from the gas expelled during the collision (visualise this by water being ejected from a pool when a stone falls in: the ejected water grows through surface tension into larger drops as it flies through the air). Observed examples of such collisions are the Antennae or the Tadpole galaxy. The matter is expelled in the form of tidal arms or tidal tails.

Indeed, in the Tadpole a number of new dwarf galaxies can be beautifully seen along the tidal arm. A recent research paper has studied the occurrence of such systems of tidal-tail star clusters and dwarf galaxies in the real universe (Mulla et al. 2011, ApJ). There are many other research papers reporting the observed formation of tidal dwarf galaxies in interacting galaxies.


Movie of the formation of TDGs in a galaxy interaction by Wetzstein, Naab & Burkert (2007), taken from the TDGBonn2009 conference website.

The number of such tidal-dwarf galaxies (TDGs) formed  has been calculated within the LCDM model. This is possible because one can compute the typical rate with which galaxies collide in the model. This number of TDGs turns out to be so high that all dwarf elliptical (dE) galaxies should be such TDGs (Okazaki & Taniguchi 2000). And it has been shown that the TDGs do not disappear – they do not dissolve because of the star formation activity within them (Recchi et al. 1997) nor can they be destroyed as they orbit around the host galaxy (Kroupa 1997; Klessen & Kroupa 1998). TDGs survive and dynamical friction is ineffective for TDGs with mass smaller than about 10^8 solar masses so that they do not fall back onto their parent galaxy.

Further, nature uses other ways of making even more dwarf galaxies: A disk galaxy plunging through a galaxy cluster is known to be stripped off its gas by the hot intra-cluster gas. A Japanese group has recently found star-formation in dwarf-galaxy sized objects behind such a disk galaxy from gas stripped from the host galaxy (Yoshida et al. 2008).  They refer to these dwarf galaxies as “fireballs”.

TDGs and fireballs are objects that look like galaxies although they cannot contain much dark matter. They form as dwarf irregular gas-rich galaxies, and are rotationally supported dwarf disk galaxies, because the orbiting gas in the tidal arm is accreted onto the self-generated gravitational potential. Once formed, such a galaxy would remain like a dwarf irregular galaxy if it escapes (Hunter, Hunsberger & Roye 2000, ApJ), or if it remains in orbit about the parent or host galaxy, it will evolve to a dwarf ellitpical (dE) or dwarf spheroidal (dSph) satellite galaxy: Because of tides acting on it from the host, its gas is channelled to its central region where it forms stars and/or the gas is stripped through ram-pressure from the hot gas around the host galaxy.

Thus Okazaki & Tanigushi’s work shows that if LCDM is right, then so many TDGs are produced as to account for all known dE galaxies, not even counting the fireballs.

This is catastrophic for LCDM because it means that there would be no dark-matter dominated dwarf galaxies (TDGs cannot have dark matter because they cannot capture many dark matter particles as shown by Barnes & Hernquist 1992, Nature). Note that the absence of dark matter is nicely consistent with the observation that dwarf elliptical galaxies indeed are not dark matter dominated (Toloba et al. 2011).

We thus have an empirical confirmation of Okazaki & Taniguchi’s work: dE galaxies indeed do not require a dark matter content.  This leads to the Fritz Zwicky Paradox which we have dealt with on two past occasions: I. The Fritz Zwicky Paradoxon and II. The Fritz Zwicky Paradoxon and its solution.

Now, a convinced LCDM cosmologist might just trivially reply: If we define a galaxy to be a gravitationally bound system with dark matter, then, clearly, for dE “galaxies” to be galaxies, the dark matter must be at larger radii where it does not affect the motion of the stars. This is clever: we can simply move the invisible dark matter away from the central region where it should really be so it cannot be detected through the motions of the stars. And the physics responsible for this expulsion of dark matter is largely unknown, but is speculated to be due to the energy radiated by stars (stellar feedback) or orbiting gas clumps (note that all attempts to show this actually works have failed unless unrealistic assumptions are made).  But that is Ok, because small-scale physics is gastrophysics or weather anyway. That this scientific trick is actually being applied can be seen in this research paper.

3) For example: The Local Group and the similarity of disk galaxies

The Local Group of Galaxies is dominated by two major disk galaxies that are similar and which are in similar massive dark matter halos and which have similar satellite galaxy populations.

How likely is the formation of such a group with its generic properties according to the GR+I+CDM+DE model? It turns out to be very unlikely: less than 0.01 percent !!

This statement is based on the LCDM models of Milky-Way (MW) type galaxies in comparison to real galaxies. It results from selecting, in a computer model of the universe, those dark matter halo masses which are of similar mass to that of the Milky Way galaxy and then calculating the fraction of galaxies that are of similar brightness as the Milky Way or Andromeda.

Noteworthy here is that in their abstract Libeskind et al. (2009), who did just such cosmological computations, suggest MW-type galaxies with a similar satellite population occur often, about 35 per cent of the cases. This would suggest that the case of a group consisting of two such major galaxies and their satellite systems (like the Local Group) is not a rare case at all!

This apparent contradiction can be explained by noting that Libeskind et al. quote in their abstract numbers for a subsample of halos that also have to fulfill a number of other criteria. These must not be omitted when calculating the probability to find a galaxy like the MW inside a halo of the appropriate mass. Let us have a closer look:

Consider all halos with a mass similar to that of the MW, i.e about 10^12 Solar masses. Only about 10 % of these halos contain a galaxy of the brightness of the MW. About 14 % of these galaxies fulfill a second condition, namely that they have least 11 dark-matter-dominated but luminous satellites, like the MW. And it is 35 % of these simulated galaxies, which also fulfill a third condition, namely that the dark-matter-dominated lumninous satellite galaxies of the host galaxies move in a similar way to the ones of the MW. Thus, the probability for a halo with 10^12 Solar masses to fulfill all three conditions (like the MW) is 0.4 %.

Now consider the halo of the Andromeda galaxy. It is of similar to that of the MW and observations of the Andromeda galaxy show that this halo fulfills at least the first two conditions mentioned above. The probability for that is 1.4 %.

Finally, consider the Local Group. With just the masses of the two dominant halos given (namely the halo of the MW and the halo of Andromeda), the probability to have them populated with the two observed galaxies is 0.4 per cent times 1.4 per cent = 0.01 per cent (see Kroupa et al. 2010 for details).

These small likelihoods come about because in LCDM a present-day dark matter halo is build-up from a very large number of mergers of somewhat smaller halos, a process that is known as hierarchical merging. The galaxy that lives inside the halo is the result of how much and in what way the normal matter gets into the halo. A halo can be in a dense region suffering many encounters and mergers, it can be fed by one or many filaments, or it can be in a quite sparse region.

To stand a chance to actually get a Milky-Way type galaxy, a recent study by Agertz, Teyssier & Moore (2011) of forming disk galaxies in the GR+I+CDM+DE model needs to perform a trick. The authors select a cold dark matter halo which did not suffer many mergers: Near the beginning of their Section 3 they state:

The halo has a quiet merger history, i.e. it undergoes no major merger after z= 1, which favours the formation of a late-type galaxy.

But while this is an exception in the GR+I+CDM+DE model, which is a severe problem for this model in which galaxies strictly form through hierarchical merging, Prof. Mike Disney has shown in his paper with the title “Galaxies appear simpler than expected” (Disney et al. 2008, Nature). They write:

More generally, a process of hierarchical merging, in which the present properties of any galaxy are determined by the necessarily haphazard details of its last major mergers, hardly seems consistent with the very high degree of organization revealed in this analysis. Hierarchical galaxy formation does not explain the commonplace gaseous galaxies we observe. So much organization, and a single controlling parameter which cannot be identified for now, argue for some simpler model of formation.

Thus, real disk (or “late-type”) galaxies, which comprise nearly 80% of all galaxies, show far less variation than would be expected from simulations of galaxy formation within the LCDM-model.

Or to put it differently: The fact that the two dominant galaxies of the Local Group are so similar is apparently nothing exceptional, whereas the LCDM-model suggests that two dark matter halos of similar mass are expected to harbour very different baryonic galaxies. We call this the Invariant Galaxy Problem.

4) For example:  The Disk of Satellites (DoS)


The distribution of “classical” (yellow) and faint (green) satellite galaxies around the Milky Way (blue). From Kroupa et al. (2010).

How are the satellite galaxies distributed generically?

For example, can the disk of satellites of the Milky Way be accounted for by the LCDM model? And, why do the 13 newly found satellites with very different discovery histories using very different observing techniques with very different biases end up defining the same disk as the 11 bright classical satellites?

Our MW has a diameter of about 50kpc. Around it are about 24 satellite galaxies (about eight more are likely to be discovered on the Southern hemisphere since the North- and South-Galactic distributions must be about symmetric).

The 11 brightest of these, which have been largely found using photographic plates and are known since a long time, are in a disk-like structure with a diameter of about 500 kpc and a thickness of about 50 kpc (the Disk of Satellites, DoS). This disk of satellites sits nearly perpendicularly on the 50 kpc sized MW disk.

What is strange is that the 13 newly found satellites, all of which are very faint and so can only be discovered using computer-aided digital sky surveys to find the few faint stars that belong to a new satellite galaxy, are also distributed in this same DoS (Figures 4 and 5 in Kroupa et al. 2010). Now, why on Earth are these very faint satellite galaxies, which have completely different discovery histories and methodology, distributed just like the bright ones? The SDSS survey volume used to find the very faint satellites is a cone on the Galactic sky on the Northern celestial hemisphere. This is why some astronomers would erroneously say that the very faint satellites follow an anisotropic distribution because the survey volume is not spherical.

This is wrong. It is wrong because if the survey volume were to be the cause for the observed anisotropy of the very faint satellites, then we would need to ask why the survey volume happens to follow the DoS of the bright satellites? In fact, this is not the case, because the survey volume is a more or less roundish cone rather than a stripe on the Galactic sky.

The only physically plausible reason as to why the very faint and the classical, bright satellites define the same DoS independently of each other is that they are related to each other. That is, they are correlated in phase-space. Such a high degree of correlation is simply not possible in the standard LCDM model, because in the model most of the satellite dark matter halos fall-in individually and orbit on independent orbits about the MW. At best a small group of satellites could fall-in together, forming, for some time, a phase-space correlated sub-population. But this amounts to not more than a handfull of satellites, if at all. In order for such a group to remain identifiable as a DoS in the MW halo, the group would have to have fallen in only recently, at most a few Gyr ago. Such group infall has been postulated by a few authors to explain the DoS, but this proposition fails because the required diameter of such a group must be less than 50 kpc in order for the group to remain in a DoS which is about 50 kpc thick. Metz et al. (2009) have, however, shown that such groups of dwarf galaxies do not exist in the real universe.

5) For example:  Contradictions between LCDM research groups

The missing satellite as well as the DoS problem are very serious issues for LCDM which is why an impressive effort is undertaken world-wide to seek solutions within LCDM. It turns out that different research groups “solve” the satellite problem of the Milky Way independently of each other. But, it also turns out that the solutions are mutually exclusive, that is, they contradict each other.

For example,

Deason et al. (2011, MNRAS, in v1 of the electronic preprint) suggest a solution: In their abstract:

We attribute the anisotropic spatial distribution and angular momentum bias of the satellites at z=0 to their directional accretion along the major axes of the dark matter halo. The satellite galaxies have been accreted relatively recently compared to the dark matter mass and have experienced less phase-mixing and relaxation — the memory of their accretion history can remain intact to z=0.

On the other hand, Nichols & Bland-Hawthorn (2011, ApJ) also solve the satellite problem but ignore the spatial anisotropy (i.e. DoS) problem. In their abstract we read:

This model of evolution is able to explain the observed radial distribution of gas-deficient and gas-rich dwarfs around the Galaxy and M31 if the dwarfs fell in at high redshifts (z~3-10).

This example demonstrates that only small aspects of the whole problem can be solved. For example that the satellite galaxies of the milky Way are gas poor can be understood if their gas was stripped, but this then requires them to have fallen in a long time ago. On the other hand, to explain the DoS the satellites must have fallen in recently …

It demonstrates that an overall consistent solution within LCDM does not seem possible.

6) For example:  The internal propertis of satellite galaxies

A major failure comes from the internal properties of the satelllite galaxies. There are two tests:

A) As stated above, the law of energy conservation is a fundamental property of physical systems. For satellite galaxies this implies that dark matter sub-halos (that end up hosting visible satellite galaxies) which are more massive or heavier can gather more normal matter and will therefore make more stars and will therewith appear brighter. On average! It needs more energy to remove gas from a more massive satellite dark halo. A heavy dark matter sub-halo may also suffer a catastrophic encounter with the host dark matter halo central density if it is on a very radial orbit such that it may loose a large fraction of its own dark matter halo. But, on average, a heavier dark-matter halo must host a brighter galaxy. How much brighter a satellite galaxy with a heavier dark matter halo is can be calculated in LCDM.

Many groups have done this automatically when they study satellite galaxies in their LCDM models. In our paper (Kroupa et al. 2010) we tested this correlation between model satellite brightness and the dark matter halo mass for all existing recent models, and every single one of the models shows a significant, i.e. pronounced, relation: Heavier model cold dark matter halo masses host brighter model satellite galaxies.

One can also measure the dark matter halo masses of the real satellite galaxies by observing the motion of their stars: the stars move more quickly than they should and this can be explained either with non-Newtonian dynamics (e.g. MOND or MOG), or with a cold dark matter halo in the standard LCDM model.

The result is that the real satellite galaxies all have the same cold dark matter halo masses, although they have a vast range of brightnesses. Each weighs about 10^9 solar masses, and the mass in stars ranges from 10^3 solar masses to about 10^7 solar masses.  We calculated the probability that this would be the case if the LCDM model were correct, and this probability turns out to be so small that the LCDM model needs to be discarded just based on this one test alone!!

That is, the dark matter halo masses of the satellite galaxies are unphysical. There are no dark matter halos around the satellite galaxies.

B) The second independent “internal-satellite property” test: Ignoring the previous result: if the satellites were embedded in their dark matter halos, each of which weighs about 10^9 solar masses, then the visible, bright satellite galaxy which sits deeply inside this dark halo, would be typically well-shielded against external tidal fields, especially so if the satellite galaxy is more than 100 kpc away from the Milky Way.

The stars in each of the satellites are observed to move with about 7 km/s = 7 pc/Myr (compare: the Sun moves with about 220 km/s about the Milky Way centre). Thus, in 100 Myr each star has moved once through a typical satellite galaxy, since the visible parts of them are only a few hundred pc large. So after a few 10^8 yr the stars in a satellite galaxy are fully mixed throughout the visible satellite.

If, at some time, there was a structure in the satellite, this structure would smear apart in a few 10^8 yr. Since the satellites are about 10^10 yr old, and since they orbit around the Milky Way in about 10^9 yr, essentially all of them should look very smooth and round. For example, globular clusters are smooth and round because of this same reason – the stars phase-mix away any possible sub-structure within the time it takes for a typical star to move through the cluster (about a million years) or satellite galaxy (a few hundred million years).


The Hercules dwarf galaxy, a satellite of the Milky Way. Fig. 6 from Kroupa et al. (2010).

But, it turns out that many of the satellite galaxies look squashed, disturbed, distorted, asymmetrical and some have bumps in them. An example of a satellite more than 100 kpc away is provided in Fig.6 of Kroupa et al.(2010). And as another example Palma et al. (2003) document the peculiar morphology of Ursa Minor dSph satellite. Fornax, the brightest satellite, which lies about 140 kpc away from the Milky Way, has an off-center density maximum, appears squashed and has a twisted inner appearance (Demers et al. 1994). In the Dark Matter Debate Simon White put Fornax forward as a satellite which fits the LCDM model best of all satellites in terms of its derived dark-matter mass. But clearly, this is not consistent with its complex inner structure. These are only three examples of many.

Thus, the satellites cannot be contained in the large and relatively massive (10^9 solar mass) dark matter halos which are a central feature of the LCDM model.

So again we arrive at the same conclusion, but using entirely independent evidence: the dark matter halo masses of the satellite galaxies are unphysical – the stellar motions have nothing to do with cold dark matter halo masses.

But, if the satellite dark matter halos are unphysical, then the whole LCDM model collapses, because the Milky Way would violate the requirement by the model to have dark matter dominated satellite galaxies.

7) For example:  dwarf galaxies in LCDM don’t match real dwarf galaxies

Understanding the properties of dwarf galaxies in general is another major problem in LCDM. For example, Sawala et al. (2011) write in their abstract:

We present cosmological hydrodynamical simulations of the formation of dwarf galaxies in a representative sample of haloes extracted from the Millennium-II Simulation.

[. . .]

The dwarf galaxies formed in our own and all other current hydrodynamical simulations are more than an order of magnitude more luminous than expected for haloes of this mass.

8) For example:  the downsizing problem

Related to the above problem, in LCDM dwarf dark matter halos form first and later some of them merge such that massive dark matter halos appear later than the dwarf ones.

Since baryons follow the dark matter a prediction (using this term correctly) of LCDM was that dwarf galaxies should be older on average than the bright massive galaxies. This turns out to be completely wrong.

What the observations told us is that dwarf galaxies are typically younger than the massive galaxies.  This is referred to as the downsizing problem.

In order to solve this problem, the LCDM  community needed to invent mechanisms that delayed the formation of stars in dwarf halos while enabling massive galaxies to emerge quickly after the Big Bang. One possibility would be to postulate that in dense environments stars formed quickly as the massive elliptical galaxies were assembling, while dwarf halos in less-dense regions could not form stars because the gas was still too hot or was heated from various sources.

A problem with this ansatz is that actually denser regions have a higher star-formation activity since there is more denser gas. This leads to local heating which is supposed to suppress star formation in order to allow disk galaxies to form without bulges: early supernovae heat up the gas which then needs time to cool. It will then slowly accrete onto the galaxy. So massive galaxies should not form so rapidly.

In low-density regions on the other hand, where the dwarfs ought to form, there are no major heating sources to stop gas cooling into the dwarf halos. So the dwarfs should form quickly.

The resulting models are messy, and usually they cannot account for the whole galaxy population. See for example Guo et al. (2011) and/or Firmani & Avila-Reese (2010).

Downsizing is not solved to this date.

9) For example:  disk galaxies are too bulgless

Even worse (for the GR+I+CDM+DE model), between 58 to 74 % of all real (observed!) disk galaxies do not have a bulge, as demonstrated only recently by Kormendy et al. (2010). They write in their abstract:

“We conclude that pure-disk galaxies are far from rare. It is hard to understand how bulgeless galaxies could form as the quiescent tail of a distribution of merger histories. Recognition of pseudobulges makes the biggest problem with cold dark matter galaxy formation more acute: How can hierarchical clustering make so many giant, pure-disk galaxies with no evidence for merger-built bulges”

But, calculations in the LCDM model have always been showing that the vast majority of galaxies have large bulges or are spheroidal altogether. For example, Piontek & Steinmetz (2011, MNRAS), write in their abstract:

“A mechanism to create bulge-less disc galaxies in simulations therefore remains elusive.”

This is because in the LCDM model, structures grow hierarchically by the merging of countless smaller sub-structures. When the different sub-structures merge, their kinetic energy is used up in heating the gas in these sub- structures. In the end, the gas cools down again by radiating the energy away and sinks towards the center of the whole object. But this resulting object assumes a spheroidal shape through these processes rather than forming a large thin rotationally supported disk. All computations show this to be the case. The only way to halt the infall of too much gas is to blow the object apart by supernovae or artificially enhanced star formation and stellar feedback. But, the models created to do this are unphysical.

For example, here is a recent state-of-the art research paper in which the authors state in their abstract  “Photometric decompositions thus match the component ratios usually quoted for spiral galaxies better than kinematic decompositions, but the shift is insufficient to make the simulations consistent with observed late-type systems” (Scannapieco et al. 2010).

10) For example:  Dark matter emergence problem: a conspiracy

Notwithstanding the above major problems within the LCDM model to account for most observed galaxies (well, for galaxies in general actually), there is yet another significant unsolved problem, namely the Dark Matter Emergence Problem:

In any galaxy, dark matter always only appears when the surface density of normal matter falls below a critical value, as demonstrated by Gentile et al. (2009, Nature). Now note that the acceleration is proportional to the surface density of a galaxy with Newtonian gravitation. Also note that the transition from Newtonian dynamics to MOND is set by a critical acceleration (and thus a critical density). It is interesting that according to Gentile et al.’s analysis, dark matter magically appears in real galaxies only below this critical density.

This is natural in MOND, but within the LCDM model there is not a single clue based on known physical principles that may give rise to this observed fact. Is this not a strong hint?

This is problem very closely related to the Conspiracy Problem, which has already been  discussed in Question A. It is an old problem of the LCDM model, and despite decades of computer simulations using ever improving and ever faster machines, absolutely no remedy is on the horizon.

11) For example:  Voids

Yet other tests include: how empty are the voids, notably in the Local Volume, and can the observed emptiness be reconciled with the sub-structures that must be there in the model? Again, this is a major problem unless other parts of the model are upset (e.g. one could force the void sub-structures to remain dark, but then the galaxies in the sheets would have wrong properties). This is emphasised by Peebels & Nusser (2010, Nature). They write:

“We conclude that there is a good case for inconsistency between
the theory and our observations of galaxies in the Local Void.
Conceivably, the local sample is atypical; this will be checked as
galaxy surveys improve. Perhaps survival of detectable galaxies is less
likely in the Local Void, although that is not supported by the
depleted state of dwarfs near large galaxies. Or perhaps we are learning
that growth of structure is more rapid than predicted in the
standard cosmology, more completely emptying low-density regions.”

They also emphasise that there are too many really large galaxies just outside the main sheet, writing:

“30% of the largest galaxies are more than 2 Mpc above the Local Sheet. If galaxy luminosities were randomly assigned, this situation would have a 1% probability, but the probability is less than this in the standard
picture of the cosmic web, in which more-luminous galaxies avoid less
dense regions. These three could not be dwarfs masquerading as large
galaxies; their circular velocities indicate the central masses of large
galaxies. That is, the presence of these three large galaxies in the
uncrowded region above the Local Sheet is real, and at well below 1%
probability it is an unlikely consequence of standard ideas.”

12) For example: A large fraction of normal matter is missing

The missing baryon fraction: Within the Big Band LCDM model we know precisely how many atoms of normal matter were produced during big-bang nucleosynthesis. These calculations are in good agreement with the fraction of Helium among all Hydrogen observed, but fail to account for the amount ot Litium observed. But, even worse, most of the atoms that ought to have been created just after the Big Bang have not yet been found. Astronomers do not know where the majority of normal (baryonic) matter is (e.g. McGaugh 2007) – it has gone missing.

13) For example: Big Bang nucleosynthesis . . . ?

Big Bang nucleosynthesis makes the wrong Lithium abundance, as has been emerging ever more clearly. See this recent New Scientist contribution, and quoting from it:

“One thing that everyone does agree on is that things are getting worse. “The lithium-7 problem is more serious than ever,” says Joseph Silk at the University of Oxford. “

Here is a research paper addressing this issue: Cyburt et al. (2010).

Concluding Remarks:  Either we live in a Bubble of Extreme Exception or  LCDM is wrong

We have seen that a massive computational effort by many groups has been able to quantify the distribution of matter on scales of 10 Mpc and less. The standard cosmological model turns out to not be able to account for the observed distribution of matter on these scales. Meanwhile, new dynamical laws have been discovered which are extremely successful in accounting for the appearance and motion of matter on galactic scales and above – see Question C.II: MOND works far too well (will be on line soon).

Especially noteworthy is that in all of the tests performed in our research paper LCDM fails. And, above many additional failures are documented.

The likelihood that the observed data can be modelled by the LCDM model is very small for each test. Taking the tests together implies that LCDM is completely ruled out, or, one may conclude that we live in a Bubble of Extreme Exception (the BEE hypothesis to save the LCDM hypothesis).

We thank Joerg Dabringhausen for useful comments. By Pavel Kroupa and Marcel Pawlowski (08.03.2011). See The Dark Matter Crisis.