Question C.III: Fundamental theoretical problems

Rather than being posted “soon after” II: MOND works far too well ! (published on the 21.03.2011), a delay caused by internal university issues arose. We are back though, for the time being, with the originally advertised “Question C.III: Fundamental theoretical problems” (this contribution).

To re-iterate: what is the purpose of this series on SciLogs? We are aiming to document, within the time we have for such matters, the already noticeable paradigm shift away from a dark-matter dominated Einsteinian inflationary cosmology model to a different description which may, or may not, be fundamentally based on Einstein’s GR theory.

Continuing now with Qestion C.III:


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 had been 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 !

III: Fundamental theoretical problems  (this contribution)

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 III, 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 III. Ctegories I and II can be found in seperate contributions as outlined above.


III) Fundamental theoretical problems

The mathematical foundation of the model is very problematical. It relies on too many completely unknown “new physics”: inflation, cold dark matter and dark energy. Each of these has major problems. The reader is pointed to the review by Afshordi 2012 who addresses these issues accessibly but also in in much more depth.

Inflation is not understood from a particle physics point of view.For an introduction see this Wikipedia article, the 1999 article by Andrew Liddle and his documentation on the web. In his paper “Unconventional Cosmology” Robert Brandenberger provides a good overview of Inflation and its problems, and Starkman et al. (2012) show that the CMB fluctuations appear to be incompatible with the SMoC causing major tension with standard inflationary cosmologies.

Dark matter is very hypothetical, has not been discovered yet despite decades of search whereby all of the until now favoured dark-matter-particle properties have already been experimentally excluded (see Stacey McGaugh’s compilation “Cold Dark Matter and Experimental Searches for WIMPs). And, since it is not behaving as it ought to be, as inferred from direct observed properties of galaxies, additional “dark”, i.e. unknwon, forces need to be postulated to exist to arrange a model LCDM galaxy to look like a real galaxy, e.g. to “solve” the Conspiracy Problem or the MOND behaviour of galaxies (see Questions C.I and C.II).

The extensive effort world-wide to detect DM particles in terrestrial experiments has so far not been successful (e.g. Baudis & for the XENON Collaboration 2012). For example, the CRESST-II DM search has reported a possible detection of a CDM particle signal (Angloher et al. 2011), but their fig. 13 also shows this putative signal to be in the parameter region excluded by the CDMS-II (CDMS II Collaboration, Ahmed et al. 2010) and XENON100 (Aprile et al. 2011) DM-particle experiments. The search for a DM-particle-annihilation or DM-particle-decay signature from regions where high DM densities are measured assuming Newtonian dynamics to be valid has also been unsuccessful (e.g. the MW satellite galaxy Segue 1 has the highest DM density known but no DM signal has been detected, Aliu et al. 2012). Increasing loss of confidence is suffered by the experiments having to postulate ever decreasing interaction cross sections for the putative DM particles, significantly below and away from the originally favoured ones.

This is at the same time a fallacy of the adopted procedure: The existence of DM particles can never be disproven by direct experiment because ever lighter particles and/or ever smaller interaction cross sections just below the current detection threshold may be postulated for every non-detection. There exists no falsifiable prediction concerning the DM particles.

Dark energy (DE): The fluxes (i.e. brightnesses) and redshifts (i.e. distances) of observed type Ia supernovae (SNIa) do not match the cosmological models (Riess et al. 1998, Schmidt et al. 1998, Perlmutter et al. 1999) unless the universe is assumed to expand at an ever larger rate. To account for the implied accelerated expansion DE is introduced. But, as with inflation, while mathematically allowed, it remains unclear if DE constitutes physics (see e.g. the discussion in Afshordi 2012).

DE has major fine-tuning problems and is supposedly unstable to quantum corrections (e.g. Shanks 2005, “Problems with the Current Cosmological Paradigm”). Plus, a universe with DE is not energy conserving – energy appears “magically” all the time with the increasing volume of the expanding universe. This is actually well known (Kroupa et al. 2010) and would appear to be unphysical. To account for this issue one would need to postulate that the universe is not a closed system, i.e. that there is much more to it than we know (that is, yet again resort to another “dark outside” would be necessary).

Indeed, DE may not even exist, resulting from integrating a supernova (SN) Ia photon’s path across the universe without correctly adding the non-linear general-relativistic sequence of time delays and spatial contractions as the photon traverses through the inhomogeneous matter distribution between the SN Ia and the observer. An observer, who does the calculation or averaging along the photon’s path wrongly would indeed deduce falsly that the universe is larger than it ought to be, thus wrongly deducing the effect of an acceleration driven by DE. This has been shown to be quite possibly the case by Wiltshire (2007).

Thus, the SNIa flux–redshift data may at least partially be explained with an inhomogeneous universe(Wiltshire 2009, Smale & Wiltshire 2011, Marra & Pääkkönen 2012) rather than with DE, whereby systematics in SNIa light curve fitting remain an issue (Smale & Wiltshire 2011). Bull & Clifton (2012) find that the “appearance of acceleration in observations made over large scales does not necessarily imply or require the expansion of space to be accelerating, nor does it require local observables to indicate acceleration.”

It might perhaps be surprising that a homogeneous model universe should lead to a perfect agreement with the observed SNIa data. In other words, the SNIa data that stem from the real inhomogeneous universe should show some deviations from the homogeneous model. If none are seen then this may imply an over-constrained model.


What is gravitation?

It needs to be emphasised time and again that the failure of the CCM is not surprising as it is synonym with the well-known fact that gravitation is not understood. While Einstein paved the way for viewing space-time as a dynamic non-absolute physical object, we still do not know how mass emerges, nor whether inertial and gravitating mass are or should be the same, nor do we understand how space and time emerge or what they really are. We do not yet have a description of space, time and gravity on the quantum scale.

In this context, the  recent break-through by Erik Verlinde who has shown that gravity may be a pseudo force which emerges “from the statistical behavior of microscopic degrees of freedom  encoded on a holographic screen” (citing from Entropic gravity). Gravity is derived by combining thermodynamics with the holographic principle.

Interestingly, in their recent paper on “Entropic corrections to Newton’s law”,  Modesto & Randano (2010)  suggest that Verlinde’s approach leads to MONDian behaviour. Citing their abstract:

It has been known for some time that there is a deep connection between thermodynamics and gravity, with perhaps the most dramatic implication that the Einstein equations can be viewed as a thermodynamic equation of state. Recently Verlinde has proposed a model for gravity with a simple statistical mechanical interpretation that is applicable in the non-relatvistic regime. After critically analyzing the construction, we present a strong consistency check of the model. Specifically, we consider two well-motivated corrections to the area-entropy relation, the log correction and the volume correction, and follow Verlinde’s construction to derive corrections to Newton’s law of gravitation. We show that the deviations from Newton’s law stemming from the log correction have the same form as the lowest order quantum effects of perturbative quantum gravity, and the deviations stemming from the volume correction have the same form as some modified Newtonian gravity models designed to explain the anomalous galactic rotation curves.


Concluding Remarks:

Thus, the LCDM or standard/concordance-cosmological model (i.e. the CCM) relies to more than 95 per cent on unknown physics. The theoretical basis for the unknown physics is shaky at best. This is perhaps something one could live with, even though the whole construct is highly unsatisfying, if the actual predictions were consistent with reality.

But they are not (see Question C.I).

That the CMB and Big Bang nucleosynthesis as well as the motions of matter on galactic scales can be explained by a different cosmological model, one not based on the existence of cold or warm dark matter and thus probably not on Einstein’s GR theory, is already well documented in the refereed scientific literature through the work of a young generation of very talented and imaginative physicists (for an account see Kroupa 2012: “The dark matter crisis: falsification of the current standard model of cosmology”).

So, a part of the community is developing a better model. Such work is underway but is hindered not only by the complexity of its very nature, but alas also by disturbing human interventions (a book compiling personal experiences made by the mostly early-career researchers would be a valuable documentation of sociological issues at play even in our modern enlighted times).



As a final word, it is useful to recall some hostorical records.

There were, in the past, a number of instances when unknown matter was postulated to exist, on the basis of existing knowledge, and then was indeed discovered:

  1. Atoms
  2. Electrons
  3. Anti-matter
  4. Neptune
  5. the neutrino.

But there were also at least 3 cases, when unknown matter was postulated to exist on the basis of existing theory, which were however later falsified:

  1. Phlogiston (solved by thermodynamics and atomic physics = new physical laws)
  2. aether (solved by special relativity = new physical laws)
  3. a planet within Mercury’s orbit (solved by general relativity = new laws of physics)

The case with phlogiston is an interesting parallel, because well before modern concepts were in place discrepancies had arisen within the phlogiston framework such that it became untenable centuries before quantum physics allowed oxidization for example to be understood at a fundamental level.

Concerning cold dark matter, we already have exactly this same situation at hand: within the LCDM framework insurmountable discrepancies have been arising despite a practically fantastic effort to solve these, only one of them being the Fritz Zwicky Paradox. We think this is the clear signal that the CCM is not viable, and we need to move on, whereby the success of MOND is giving essential clues. As with phlogiston, while the CCM may be ruled out already and while we do have Milgromian dynamics, we do not yet have a fundamental theory of space, time and matter.


By Pavel Kroupa and Marcel Pawlowski  (31.03.2012): “Question C.III: Fundamental theoretical problems” on SciLogs. See the overview of topics in  The Dark Matter Crisis.


Author: Prof. Dr. Pavel Kroupa

I am a Czech-Australian teaching and researching at the University of Bonn on dynamics and stellar populations. After studying physics at The University of Western Australia, Perth, I obtained my PhD from Cambridge University, UK, as an Isaac Newton Scholar at Trinity College. After spending eight years in Heidelberg I habilitated at the University of Kiel, Germany. I then took up a Heisenberg Fellowship and later accepted the position as a professor at Bonn University in 2004. I was awarded a Leverhulme Trust Visiting Professorship (2007, Sheffield, UK) and a Swinburne Visiting Professorship (2007, Melbourne, Australia). In 2013 I received the Silver Commemorative Medal of the Senate of the Czech Republic, and I took-up an affiliation with the Charles University in Prague in 2016. Pure innovative science can only truly thrive in non-hierarchical societies in which competition for resources is not extreme. Therefore I see the need for the German academic system to modernise (away from its hierarchies) and warn of academic systems that are based on an extreme competition for resources (USA), as these stifle the experimentation with new ideas.

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