*(Guest post by Elena Asencio, University of Bonn, January 16th, 2021)*

It is currently accepted that structure in the Universe formed in a hierarchical way. In other words, smaller structures formed first and then merged into larger structures. The largest gravitationally bound structures in the Universe are the galaxy clusters. Since the predicted timescale in which these structures formed depends on the cosmological model adopted and, subsequently, on the gravity theory assumed, galaxy clusters can be used to test both gravity theories and cosmological models models on large scales.

In the last decades, the improvements in telescope detection capabilities have made possible to observe objects which are deeper in space. The further an astronomical object is from us, the longer it takes for its light to reach us. Therefore, deeper surveys allow us to observe how the Universe looked like in the fairly distant past. Some of the galaxy clusters that were detected in these deep surveys surpass the standard model (ΛCDM) predictions in terms of mass, size and/or galaxy-infall velocities, and could potentially pose a serious problem to the model.

El Gordo (ACT-CL J0102-4915) is a galaxy cluster with particularly extreme properties. It is located more than 7 billion light years from Earth and is composed of two sub-clusters weighing together approximately 3e15 Solar masses with a mass ratio of 3.6 and a high collision velocity of approximately 2500 km/s. Due to the highly energetic interaction of its two sub-clusters, it is also the hottest and most X-ray luminous galaxy cluster observed at this distance according to

Menanteau et al. (2012).

Figure 1: A composite image showing El Gordo in X-ray light from NASA’s Chandra X-ray Observatory in blue, along with optical data from the European Southern Observatory’s Very Large Telescope (VLT) in red, green, and blue, and infrared emission from the NASA’s Spitzer Space Telescope in red and orange. Notice the twin tails towards the upper right.Image from this source. Credits: X-ray: NASA/CXC/Rutgers/J. Hughes et al; Optical: ESO/VLT & SOAR/Rutgers/F. Menanteau; IR: NASA/JPL/Rutgers/F. Menanteau.

In our paper “

*A massive blow for ΛCDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology*” (

Elena Asencio, Indranil Banik & Pavel Kroupa 2021), we conducted a rigorous analysis on how likely it is that this object exists according to ΛCDM cosmology.

In order to do this, we searched for cluster pairs that could potentially be progenitors of the El Gordo cluster in the ΛCDM cosmological simulation developed by the

Juropa Hubble Volume Simulation Project – also known as the

*Jubilee simulation*. The reason why we searched for the El Gordo progenitors instead of directly looking for an El Gordo-like object is because extremely large objects like El Gordo require very large simulation boxes to have their number of analogues estimated in a reliable way. Larger simulation boxes have lower resolution. Therefore, when searching for El Gordo analogues in the simulation, we can not aim to match its morphological properties (e.g. the observed X-ray morphology) — as these would need a high resolution simulation with gas dynamics to be reproduced. Such simulations covering a sufficiently large volume cannot be achieved today even on the most powerful supercomputers (and are in actuality also not necessary for the present aim) — but we can try to find cluster pairs whose configuration matches the initial configuration of El Gordo in terms of total mass, mass ratio and infall velocity. To determine the values of the parameters describing this initial configuration, we need to rely on the results of detailed hydrodynamical simulations.

Zhang et al. (2015) performed a series of hydrodynamical simulations of two colliding galaxy clusters trying to find which set of initial conditions would result in a merger with similar properties to El Gordo. Among the 123 simulations that they ran for different parameters, they found that the model that gave the best fit to the observed properties of El Gordo had a total mass of 3.2e15 Solar masses, a mass ratio of 3.6, an infall velocity of 2500 km/s, and an impact parameter of 800 kpc. Models with lower mass or lower infall velocity were not able to reproduce the twin-tailed morphology of El Gordo (see Figure 1) and its high X-ray luminosity.

Using the Jubilee simulation, we found no analogues to El Gordo. We therefore relaxed the requirement of a sufficiently high mass, and found out how the number of El Gordo analogues (in terms of mass ratio and infall velocity) decreased with increasing mass. Since the Jubilee simulation was run for different cosmological epochs or redshifts, we were also able to determine how the number of El Gordo analogues (in terms of total mass, mass ratio, and infall velocity) decreased for earlier epochs or larger redshift. From these results and accounting for the fact that the total volume of the Jubilee simulation is significantly larger than the space volume in which El Gordo was found, we obtained the probability of finding a cluster pair with a similar configuration to the expected pre-merger configuration of El Gordo, at a slightly earlier epoch to that at which we observe El Gordo (see Figure 2).

Figure 2: Plot showing the frequency of analogues to the El Gordo progenitors for each position in the grid. The grid is constructed for a series of mass values in log10 scale (y-axis) and cosmic scale factor *a* (x-axis). The *a* values determine the cosmological epoch (for reference, *a* = 1 today, *a* = 0.535 at the epoch at which we observe El Gordo and *a* = 0.5 at the epoch at which we look for El Gordo progenitors, and generally the expansion factor *a* and redshift *z* are related by *a*=1/(1+*z*) ). The probability of lying outside a contour (region of fixed colour) can be expressed in terms of the number of standard deviations (σ). The higher the number of standard deviations at a certain point in the grid, the further away will this point be from the expected value of the distribution. It is generally considered that if a model surpasses the 5σ threshold, then this model is falsified. In this plot, the point in the grid corresponding to the *M̃ *and *a* values of the El Gordo progenitors is marked with a red X and it corresponds to 6.16σ. In terms of probability, this is equivalent to saying that there is a 7.51e-10 chance of finding an interacting pair of El Gordo progenitors or an even more extreme pair in the ΛCDM model.

The chance of observing an El Gordo-like object in the ΛCDM cosmology is 7.51e-10, which corresponds to 6.16σ (as a reminder: physicists accepted the existence of the Higgs boson once the experimental data reached a

5σ significance level — in general, when a phenomenon reaches a confidence of 5σ or more, then it is formally taken to be certain corresponding to a chance of one in 1.7 million that the phenomenon is untrue). This means that, assuming the ΛCDM model, we should not be observing El Gordo in the sky (but we do observe it). In fact, the tension between the ΛCDM model and the observations is even higher if one takes into account that El Gordo is not the only problematic object found in the sky.

Another well-known galaxy cluster that poses a potential problem to ΛCDM is the

Bullet Cluster. It is also an interacting cluster composed of two subclusters colliding at high velocity (3000 km/s) which, according to the ΛCDM model, is unexpected at the distance at which it is observed (3.72 billion light-years).

Kraljic & Sarkar (2015) obtained a 10% probability of finding a Bullet Cluster analogue in the ΛCDM cosmology over the whole sky. In order to get a more helpful estimate of the Bullet Cluster probability, the sky area in which the Bullet Cluster was observed should be taken into account – it would not be realistic to use the probability for the whole sky as this would imply that the Bullet Cluster was found in a fully sky survey, which is not the case. Taking into consideration that the survey in which the Bullet Cluster was found only covered 5.4% of the sky, the actual probability of observing a Bullet Cluster-like object is 0.54%, which makes it a 2.78σ outlier. Combining the probability of observing both the Bullet Cluster and El Gordo in the sky raises the tension to 6.43σ.

We also considered the possibility that the problem is not in the ΛCDM model but in the Jubilee cosmological simulation, in the

Zhang et al. (2015) hydrodynamical simulations, or in our statistical analysis. According to

Watson et al. (2014), up to now, the Jubilee simulation has been shown to work correctly in accordance with the ΛCDM cosmological model for which it was designed. So we have no reasons to believe that there might be any problems with the Jubilee simulation in that regard. We also found many lower mass analogues to El Gordo, so numerically our results should be quite sound and allow an accurate extrapolation up to the El Gordo mass. The results of Zhang et al. (2015) for the initial configuration of El Gordo are backed up by previous independent studies of El Gordo. The weak lensing analysis of El Gordo by

Jee et al. (2014) confirms the mass estimate of 3e15 Solar masses. The simulations by

Donnert (2014) and

Molnar & Broadhurst (2015) agree on an infall velocity of 2250 – 2600 km/s. Besides this, Zhang et al. (2015) had already checked that lower values for the mass and infall velocity – which would be easier to explain in ΛCDM – were unable to reproduce the morphology of El Gordo. Regarding our own analysis, in the paper we also performed the statistical analysis with a different method to check the consistency of our results. The results were indeed consistent, so we consider our methods to be reliable.

The more conservative and detailed method is shown in Figure 2.

Since the ΛCDM model cannot account for the existence of extreme objects like El Gordo or the Bullet Cluster, some authors tested other cosmological models to check how well they work in this respect.

Katz et al. (2013) searched for El Gordo analogues in a simulation that adopted a νHDM cosmological model. The νHDM model has the standard hot Big Bang, primordial nucleosynthesis, CMB and expansion history as the ΛCDM model, but assumes the extended gravity law devised by Milgrom (

MOND) and the presence of an undetected mass in galaxy clusters composed of particles like

sterile neutrinos that only interact with gravity (see the post “

Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer for a more detailed explanation of the νHDM model). Using this model, Katz et al. found that about one El Gordo analogue was expected to be encountered in their simulation box, while they could not find any analogues when they performed a simulation of similar characteristics with the ΛCDM model. Accounting for the fact that the volume of the survey in which El Gordo was found is slightly different from the volume of the simulation used by Katz et al. (2013), we determined that the number of El Gordo analogues that we expect to observe in a νHDM model is 1.16.

*Therefore, the vHDM model gets the right order of magnitude for the frequency of El Gordo-like objects.* The reason for this is that the growth of structure is enhanced in MONDian gravity, so it is more natural to find very massive objects like El Gordo at high redshift in models that assume this type of gravity.

But then, if smaller structures formed first and larger structures formed afterwards, how is it possible that we do not observe more super-massive objects like El Gordo at closer distances? The fact that structures form more efficiently in MONDian gravity also implies that larger and deeper voids will be generated with this gravity law. This prediction is in agreement with the results of

Keenan, Barger & Cowie (2013), who observationally found that the local Universe is immersed in an underdensity bubble (

the KBC void) with a radius of about one billion light years. For this reason, it is not expected that very massive objects will be able to form in the nearby regions of our Universe, as these regions will have a low density with respect to the mean density of the global Universe (see the post “

Solving both crises in cosmology: the KBC-void and the Hubble-Tension” by Moritz Haslbauer for a more detailed explanation of the KBC void).

*Therefore, the νHDM model is capable of explaining the presence of super-massive objects like El Gordo at distant epochs and is also able to explain the absence of objects like this in the local Universe.*

We conclude that El Gordo falsifies ΛCDM at 6.16σ (6.43σ if we take into account the Bullet Cluster too). We propose the νHDM cosmological model as a possible explanation to the formation of extreme objects like El Gordo or the Bullet Cluster at very early cosmological epochs. Moreover, the νHDM model also explains other observations that cannot be justified with the ΛCDM model, such as the existence of the KBC void, therewith automatically resolving the Hubble tension and accounting for the lack of super-massive galaxy clusters like El Gordo in the local Universe. Since the νHDM cosmological model automatically accounts for the observed stellar dynamics in the smallest dwarf and most massive galaxies, the rotating-planar distributions of satellite galaxies, and many other observed properties of galaxies and large scale structure, it is clear that it poses a far superior framework than the (in any case falsified) ΛCDM model for understanding the Universe.

In *The Dark Matter Crisis* by Elena Asencio. A listing of contents of all contributions is available here.