No one yet has factored in the possibility of an initial very fast speed of light, almost infinite, like gravity, which has decayed till today, initially fast, slow now. Ruling paradigm turned on its head in 2018 by Steven Robinson's PhD finding snowball earth water was hot and all rocks laid down in presence of oxygen. Cyclicity makes more sense to be read as annual, it is so identically repeated, but Triacic cyclicity twice as slow as Cretaceous, so perhaps speed of light responsible. Perhaps too radical?!

OK I just looked at the abstract, interesting. Given that under quantum chromodynamics space is now viewed, not as a vacuum but as an energy field (of Higgs Bosons), with photons of light picking up and transferring energy within that field. I assume that when light came into being, either at the command "let there be light" from the Big Boss, or by whatever non-Boss source you prefer (if credible!), the whole universe was instantly energised, with the speed of light infinite. This would also explain why, in Genesis, if God has made lots of (billions) AGNs on day 1, along with our Milky Way AGN, light has reached the embryo earth (a giant globe surfaced by water, called "the deep"), by the end of day 1, travelling 25,000 ly at present speed of light, in that time. This may be a bit radical for you, Sydney, but it fits ancient text and science. But Newton more probable than Einstein, each working to the constraints of their day?

We should take into account a closed topology of the universe.

A possible structure is generated by a homogeneous gravitational field of positve energy density. The topology is characterized by the fact, that any displacement corresponds to a rotation of the complete universe, exactly determined by the displacement.

Sydney Ernest Grimm

I am also afraid, that the discussion about the concordance of the LCDM cosmology with the large-scale structure of the universe does not make sense if it is a priori considered to be given.

It also does not make sense if the consideration a priori is restricted to a flat open topology of the universe.

It looks like a criminal case in which the detectives are exclusively authorized to look for evidence against the prejudged guilty person.

Wolfgang is right. Hot Big Bang modelling is all that it allowed for research, without trying to disprove it. A theory is only valid if it can be disproved. Other modellers, perhaps equally flawed, have been precluded from funding for decades. I don't know how long we will be assuming, but not detecting, dark energy and dark matter, without looking in a fresh direction for something else. A decay in the speed of light seems to me to be a possibility, especially as so many people are proposing it was once so much faster.

It is interesting to read these perspectives. Not many people seem willing to defend LCDM.

Investigations of large cosmic structures can be used to verify the topology of the universe. It is still not clear if the universe is flat/open or curved/closed. Clarifying this question is of dramatic importance because an open universe continuously loses mass and energy. A big bang scenario therefore is a one-shot scenario, while a closed topology allows an eternal process of energy recycling.

Blocking those investigations, for whatever reason, does not make sense.

Dear Indranil Banik,

"Is concordance LCDM cosmology consistent with the Universe's large scale structure"

Although the large local supervoid hypothesis is thought to be a logical explanation for the large scale structure of the universe, it well could be concerning large voids in general, but it does not address all the other failings of the LCDM model.

IMO Only a far older universe can explain superclusters and the web structure of the observable universe.

I see little value to the present model of cosmology: It cannot explain dark matter, dark energy, Inflation, the expansion of the universe etc. This model will almost entirely be replaced IMO. These are the related papers below that I have written concerning the failings of present cosmology, and offer alternatives to all.

https://www.pantheory.org/Technical-Papers.pdf

https://scholar.google.com/citations?user=7ONCj-kAAAAJ&hl=en#d=gs_md_cita-d&u=%2Fcitations%3Fview_op%3Dview_citation%26hl%3Den%26user%3D7ONCj-kAAAAJ%26citation_for_view%3D7ONCj-kAAAAJ%3Ad1gkVwhDpl0C%26tzom%3D480

https://pdfs.semanticscholar.org/1a50/8297574f2266cabd2d69d112f2db5b4b13bd.pdf

Yes, a fast local expansion "might indicate" a large local supervoid, but other things instead. The problem with a large local supervoid is that it breaks the cosmological principle, very dear to cosmologists. Of course, the Lambda cold dark matter model can be questioned and indeed has been questioned long before "Hubble tension" were fashionable words. For example, warm dark matter is a well studied alternative.

Jose Gaite: Our paper shows why the cosmological principle is preserved because we do not need to be at a special location in the KBC void for our model to work. Check out the section of MNRAS, 499, 2845 showing the velocity field, or the conclusions section where we also mention this. Besides, the void is observed in redshift surveys like 2MASS, of the sort used to establish LCDM in the first place. The void would help to resolve the Hubble tension perhaps, but in any case it is there.

Dear Indranil Banik, I agree that a local void is not against the cosmological principle, as long as it is not too large (not much larger than the current scale of homogeneity). I have found that a local void of 60 megaparsecs is described in Wikipedia (https://en.wikipedia.org/wiki/Local_Void). This void is already somewhat large to accomodate the current scale of homogeneity. I read that the KBC void is supposed to have 600 Mpc in diameter (https://en.wikipedia.org/wiki/KBC_Void). I think this size is ruled out by most measurements and is against the cosmological principle; assuming that the void is really void, of course.

Jose Gaite: I am not sure what you mean by 'against the cosmological principle' - if we are not at a special position in the KBC void and if there are many other such voids (which would be inevitable in the MOND scenario), then our model is consistent with the cosmological principle. The only difference is that the scale of homogeneity would be larger than in LCDM.

It would also be helpful to explain which peer-reviewed publications rule out the KBC void, which is itself directly detected in observations as discussed in Section 1.1 of our paper (MNRAS, 499, 2845) and in the original work by Keenan, Barger & Cowie:

Article Evidence for a ~300 Mpc Scale Under-density in the Local Gal...

Dear Indranil Banik, if you are saying that there are many voids of 600 Mpc, then I agree that there is no contradiction with the cosmological principle. I do not know if such scenario is inevitable with MOND (I doubt it). At any rate, it blatantly contradicts not only the LCDM but observations as well. You tell me which galaxy surveys contain many 600 Mpc voids. The Wikipedia article about the KBC void says that "it is not completely empty". It souds to me like it is not empty at all. By the way, there is a consensus on the magnitude of the scale of homogeneity.

Dear Jose Gaite: There is a part at the end of the discussion section of our article on 'other anomalies in large-scale structure' or similar. We're not saying the KBC void is totally empty, in fact it is only about 20% underdense in our best-fitting model. Redshift space distortion effects then make up the rest, allowing consistency with the 46 +/- 6% measured by Keenan+ (2013).

Galaxy surveys do typically show structure with a radius of 300 Mpc - it is just a question of how much. Tha baryon acoustic oscillation scale is about 150 Mpc, so surveys are well capable of finding fluctuations in galaxy number counts on scales of 300 Mpc. To get the actual density contrast, one has to know the so-called bias factor as usually only the brightest galaxies are probed (not the case with Keenan+ 2013, who used 2MASS - but their techniques are difficult to apply further away). Usually the bias factor is chosen to conform to LCDM expectations. But if you had a model with large voids, you could probably fit it to data. For example, the CMB cold spot might then be caused by a supervoid, as we discuss - unlikely in LCDM, but perhaps quite feasible if structure formation is enhanced while the background and CMB still behave much the same as in LCDM.

I should also mention that we tried updating some Wikipedia pages based on peer-reviewed publications, but were unable to do so for spurious reasons like we're advertising our own work. However, LCDM adherents seem to have no trouble doing the same. The bias is strong with this one. And so is the consensus, driven by hiding evidence like the well-known 2MASS survey, rotation curves of galaxies and the radial acceleration relation, satellite planes, and bar pattern speeds in galaxies, to name but a few. I don't doubt that there is a consensus about fluctuations on different scales closely following LCDM expectations, as this is the party line astronomers feel they need to toe to get ahead career-wise. However, I am interested in discussing actual peer-reviewed evidence.

Dear Indranil Banik, I have partially read your article. I am not sure I understand your reasonings. But let me begin with my own reasoning about the easier concepts.

It seems that the KBC void is, like I said, not empty at all: a 20% underdensity is hardly a void. Anyway, how probable is it that a given region of, say, 10^6 Mpc^3 is 20% underdense? This is not difficult to calculate, with the right input. However, let me caution that this calculation does not yield the probability of finding a "void" (20% underdense) of v=10^6 Mpc^3 in some survey (or N-body simulation). I have been personally involved in the theory of void finding and I can tell how subtle it is. Nevertheless, one can get an idea from the calculation of the probability that a v=10^6 Mpc^3 region is underdense.

The necessary input for this calculation is the volume dependent variance of density fluctuations. Again, this variance is subtle to know precisely, but we only need some approximate value. From my own calculations with SDSS-DR7 data, I know that the density variance for v=10^6 Mpc^3 is about 0.05, that is to say, sigma is about 0.2. Therefore, a 20% deviation is at 1 sigma and is likely. A region of 10^6 Mpc^3 has a diameter about 100 Mpc, making the KBC void not that surprising. This argument relies on just a galaxy survey and involves several approximations, but it can suggest that the KBC void is not a fluke that may conflict with standard cosmology.

I am sorry if I have misunderstood your answer or your paper. I honestly try to understand what I read. I consider hiding evidence a regrettable practice and I think that every evidence needs to be known and discussed. I am old enough to be not worried about getting ahead career-wise, so I am interested in discussing actual evidence, whether peer reviewed or not.

Dear Jose Gaite: It is subjective if you consider the KBC void 'not a void' - it will never be totally empty, and perhaps you prefer to call it the KBC 'underdensity'. I myself prefer the underdensity terminology. In any case, the model has about a 20% underdensity, and this seems to work quite well with the KBC data and the local Hubble diagram, for reasons discussed in the introduction. As for the expected cosmic variance, this is explained carefully in Section 2 of our open access paper. Briefly: the expected LCDM variance on a scale of 8/h Mpc = 12 Mpc is sigma_8 = 0.8, so on a 300 Mpc scale with fluctuations declining inversely with survey volume, you would get 3.2% fluctuations. Then allowing for redshift space distortions according to LCDM theory, this rises to 4.8% apparent density fluctuations. The apparent underdensity is in reality 46 +/- 6%, so the significance level is 46/sqrt(6^2 + 4.8^2) = 6.0 standard deviations. There is a more rigorous calculation in the article, but basically this is the result. It can be derived on pen and paper using the sigma_8 parameter from Planck cosmology papers assuming LCDM. We checked the MXXL simulation to verify this, allowing also for incomplete sky coverage. But there should be no bias, as firstly we were using stellar masses assigned semi-analytically to MXXL haloes, and secondly dwarf galaxies should not be biased tracers on such a large scale in LCDM in a survey that probes the majority of the galaxy luminosity function.

It is a little risky about considering evidence not (yet) peer-reviewed, but I agree in principle that this can be important in fast-moving areas. So in principle I am also happy to consider say a recent preprint backing up your arguments. However, you seem to be advocating the mainstream, so it is difficult to believe that such preprints would have much trouble getting through peer review quite easily. Requiring evidence to be peer-reviewed is a much greater burden on my side of the argument, though as it was, we did not get into serious difficulties with the underdensity article at MNRAS.

Dear Indranil Banik, I also prefer the "underdensity" terminology, because it is more adequate.

In regard to your calculation, let us agree on the value of sigma_8. However, I do not know from where you get that fluctuations decline inversely with survey volume. This is certainly not what I find with the SDSS-DR7 data or with the N-body simulations that I have studied. If you are using the scale dependence of the Harrison–Zeldovich power spectrum, then it is different and anyway I do not agree: you cannot apply the Harrison–Zeldovich power spectrum over the range of scales close to 8/h Mpc.

What do you exactly mean by "3.2% fluctuations"? Is it that sigma=0.032? Why the apparent underdensity is in reality 46+/-6%? Do you not say that it is 20%?

Is it not somehow contradictory that you are taking values from studies that assume the LCDM model?

Regarding the sociological aspect, I am not against peer review, of course, although I know first hand how deficient it can be. I am not advocating the mainstream or any stream whatsoever. Like I said, I honestly try to understand what I read. Believe it or not, I have a good deal of trouble to publish my own results. Here, I am just responding to the discussion that you started.

Dear Jose Gaite , I indeed mean that sigma = 0.032/ The apparent underdensity is 46 +/- 6% (this does not assume LCDM as such), while the actual underdensity is only about 20% in our best-fitting model. The difference is due to redshift space distortion - say the survey found 50,000 galaxies out to redshift 0.07, which in standard cosmology would be 300 Mpc. And suppose the apparent underdensity is 50%, calculated assuming the survey covers 0-300 Mpc. But in our best-fitting model, due to outwards peculiar velocities, the actual distance at which the redshift is 0.07 is only 250 Mpc. Then the density is 1/2*(300/250)^3 times the cosmic mean, which is inferred based on the number of galaxies at distances of say 600 - 800 Mpc where the void would have a negligible effect. So the actual underdensity would only be 14%. This redshift space distortion effect is taken into account both in LCDM (in the part of our paper on consistency with LCDM) and in MOND (where we assess consistency with MOND). It is also briefly described in the introduction, which has a more intuitive explanation.

sigma_8 is a standard cosmological parameter. While you probably can't apply it to scales much below about 20 Mpc, it should be fine at 300 Mpc. In general, the idea is that the rms density fluctuations are sigma_8*8 Mpc/(rh) at radius r, with h about 0.7. This relation is for the asymptotic tail of the power spectrum, i.e. for scales larger than about 20 Mpc which entered the horizon after matter-radiation equality. It should work quite well at r = 300 Mpc. Besides, our calculations are based on the MXXL simulation, which has a box size of 4100 Mpc, allowing us to consider many 300 Mpc radius spheres. The simple analytic estimate I provided shows why the result we obtained with MXXL is reasonable - this much more detailed analysis also gives 3.2%, as expected.

While the KBC results are obtained assuming LCDM, a correction is applied to account for what happens in the real world, according to various models. One of these is LCDM, but the other is MOND. So it is not contradictory. Besides, I would hope that observations have some meaning regardless of the cosmological model one chooses to believe. It is good that you are also trying to understand what the evidence is trying to tell you.

Dear @Indranil Banik, thanks for the explanations. I do not understand all your arguments, but I agree with the ones that I understand.

I agree that sigma(r) (the rms density fluctuation at radius r) can be approximated as sigma_8*8 Mpc/(rh) (this is very different from your preceding "fluctuations declining inversely with survey volume"). I mentioned before that sigma is about 0.2 at r=100 Mpc (from SDSS-DR7 data) and you say that sigma=0.032 at r=300 Mpc. The value 0.032 is smaller than 0.2/3, but sigma must decrease faster on larger scales. There are surely better approximations for sigma(r) than the inverse of r, but perhaps this is not important for your arguments (at any rate, the last digit in 0.032 is probably superfluous).

I cannot follow your arguments about the KBC void and redshift distortions. Nevertheless, let me point out that it seems to me that you are evaluating the mass inside the void by galaxy counting and this is very inexact.

MOND can be all right. The evidence will tell :-)

Just to clarify that the underdensity reported in the Keenan+ (2013) work is based on the luminosity density of galaxies. The majority of the luminosity function is traced. Its shape is similar at different redshifts, but the normalisation is lower at very low redshift than further away. There is no reason to expect a significant bias between the total luminosity density and the mass density on scales of 100 Mpc or more. In any case, the estimated fluctuations in MXXL are based on assigning stellar masses to haloes semi-analytically, as done by LCDM experts in previous publications. So it is fairly clear that the actual fluctuations should only be 3.2%, which becomes 4.8% apparent fluctuations after accounting for redshift space distortions. This is too little to explain the observations, which represent a 6.04 sigma outlier. This tension is independent of the Hubble tension, which also falsifies LCDM at over 5 sigma. A different Hubble constant would simply multiply the luminosity density by some factor, but would not change the fact that this is much lower at very low redshift than further away. The high curvature of the Hubble diagram (q_0 parameter) is also suggestive of a large local void.

Fine, probably there is no reason to expect a significant bias between the total luminosity density and the mass density on the relevant scales. I was thinking of "the survey found 50,000 galaxies", which suggested to me that you were only considering galaxy counts.

I have to read more about the KBC void.

I would be interested to know if the density fluctuations in SDSS are indeed 0.2 on a 100 Mpc scale. The LCDM prediction is 0.8*8/(100h), or about 0.1 - essentially triple the 0.032 we got on a scale of 300 Mpc. If the actual fluctuations are instead 0.2, this would be an important constraint. Doubling the density fluctuations compared to LCDM expectations would make the KBC void go from a 6 sigma outlier to a much more plausible 3 sigma outlier, though obviously this would involve a different theory than LCDM where the density fluctuations are larger.

Of course, I can tell you why I said that the density variance for v=10^6 Mpc^3 is about 0.05 from SDSS-DR7 data. This was actually a rough estimation from several volume limited samples that I have studied, since they do not have all exactly the same mass variance. The mass here is the stellar mass. I could get a better estimate by weighting each sample variance by the partial contribution of the sample to the total mass density.

I must insist that your "LCDM prediction" 0.8*8/(100h) is based on a rough approximation to sigma(r). Is it an approximation that is widely accepted?

Dear Jose Gaite, One does not have to use LCDM expectations calculated in such a simple way, and can instead query some simulation like MXXL in a manner similar to what we did in MNRAS, 499, 2845. The approximation would be a little off around 100 Mpc due to the baryon acoustic oscillation feature. This might be why the sample variance you mention is a little high - it might just be how LCDM works.

Good point! One can employ LCDM N-body simulations to compute directly the mass variance. I have studied several N-body simulations but I have never actually computed directly the mass variance; and it is a simple computation. The MXXL simulation is good because it has a large box length, but it does not contain baryons. I still have the Mare-Nostrum simulation data, which is older and has smaller box length but contains baryons. I can carry out the computation for baryons and CDM with it.

You say that my SDSS-DR7 mass variance is a little high because the stellar mass fluctuations reflect the baryon acoustic oscillations. Is this right?

Dear Jose Gaite, I assume so, though I am not an LCDM expert. Certainly the baryon acoustic oscillation feature has been observed and is expected in LCDM, so I suppose it should show up in SDSS. Indeed, I thought this was the whole point of the BOSS survey.

As for the stellar masses, indeed these are not available in MXXL. So these were assigned semi-analytically, as discussed in our paper. We did not do this assignment, it was done by LCDM experts and the catalogue was provided to us. You can try to compare the fluctuations in stellar mass estimated from MXXL, with fluctuations in stellar mass (in haloes above say 1e10 M_Sun as we did) obtained from a hydrodynamical cosmological simulation. However, it is very difficult to understand why there should be any difference on scales beyond 100 Mpc. While a comparison at 300 Mpc might be beyond the reach of such hydrodynamical simulations, I would imagine that any difference (or bias) is absent by the time you get to even 75 Mpc or so. Possibly there is still a small difference at 50 Mpc, and differences are significant at smaller scales.

Dear Indranil Banik, I am less familiar than you with moderately large scales. I have been mostly concerned with nonlinear structure formation. My idea about bias is that it is an obscure subject. Moreover, I have the impression that many results are hardly convincing, because they are based on fluctuations in galaxy counts, which do not represent the fluctuations in stellar mass. In some simulations, one has the real fluctuations in baryon mass, but any assignment of stellar mass seems to me too model dependent. However, if one is trying to distinguish very different predictions, perhaps it can do it. I do not know.

I should clarify that the first paper I mentioned on the local underdensity deals with very large scales that in LCDM should be well within what is termed the linear regime. Certainly non-linear effects are not supposed to be significant at a scale of 300 Mpc.

It is also true that results based on just probing the high end of the galaxy luminosity function may well be inaccurate. Indeed, the section near the end discussing objections to the void scenario discusses this. The agreement between LCDM expectations for cosmic variance and observed fluctuations in galaxy counts typically requires the assumption of some bias factor. While some bias may well be expected, it is not known a priori exactly how much there should be. As a result, this is not a very strong test of LCDM, since it is possible to choose the bias factor such that it works. To make matters worse, the observed galaxy number density fluctuations are often used to guide the choice of subgrid feedback prescriptions in simulations like Illustris. Which is why the gold standard of science is to make correct a priori predictions. Very deep and extended voids with approximately 300 Mpc size were predicted a priori in MOND by Angus & Diaferio (2011) and Katz+ (2013), as discussed also in our article on El Gordo. In general, structure formation is expected to be enhanced in MOND due to the longer-range gravitational interaction.

Although the galaxy bias issue (mismatch between density contrasts in the galaxy distribution and that of the total matter) can be important at smaller scales, they should really not affect the KBC results as these involve the majority of the galaxy luminosity function and are on a very large scale. It would also be unusual for incompleteness effects in a survey to cause it to discover a local underdensity, since observations are generally easier for closer by galaxies. Such incompleteness effects would rather give the appearance of a local overdensity. However, the 2MASS observations are fairly complete over the majority of the luminosity function, so there should not be artificial effects like a local overdensity or underdensity unrelated to the actual density contrasts. There is also a lot of other evidence for a 300 Mpc scale local underdensity from other surveys, as discussed in the introduction to our underdensity article. I do expect SDSS to reveal other problems with LCDM regarding large scale structure, but not if it is a question of comparing observations with theoretical where it is possible to put in an arbitrary multiplicative factor in front of the latter. One of the few fairly direct tests of large scale structure is perhaps the weak lensing cross-correlation power spectrum.

Dear Indranil Banik, I do not know how justified your statements are, because I am not sufficiently expert on the issues. Let me make a few remarks.

Indeed, scales over 100 Mpc are linear or very mildly nonlinear in the LCDM model. A 40% underdensity is mildly nonlinear.

The bias factor is already necessary to account for any variance between the non-baryonic dark matter and baryon distributions. The latter is supposed to be better known than the former, but most data about the large-scale baryon distribution come from galaxy surveys that do not even have stellar masses assigned. I do not think that there is any theory that relates the total mass density to the galaxy number density. Therefore, I agree that what is usually done is to assume some kind of bias factor to make the LCDM predictions work.

Of course, weak lensing is a direct observation of dark matter. I do not know enough about its current status to decide if it has provided definite and complete information on the bias factor.

In regard to the KBC void (or underdensity) as a fluke, I must insist that the probability that a given random region is, say, 40% underdense is smaller than the probability of finding some 40% underdense region in a larger region, especially, if this is a much larger region.

I cannot follow the introduction to Milgromian dynamics in your paper, so I may now ask a naive question. Anyway, it bothers me that you say that MOND is capable of accomodating the KBC underdensity whereas LCDM is not. I understand that MOND is actually a sort of modified gravity theory and these theories have many free parameters. To what extent is the model that you favor parameter free?

I thought I would clarify a few things related to my original post. Firstly, it is true that the KBC underdensity is not measured with respect to the average luminosity density of the whole Universe, since this is not really known observationally. However, figure 11 of their paper (ApJ, 775, 62) shows that the luminosity density reaches a plateau between 400 - 800 Mpc, where the data runs out. This is presumably the average luminosity density of the whole Universe. If not, then the region at 40 - 300 Mpc might be much closer to the cosmic mean - but all the data points covering 400 - 800 Mpc would then have to be interpreted as showing a density about double the cosmic mean. This is a much larger density perturbation in fractional terms. Given also the larger volume, it would be even less likely for LCDM to have a shell 400 - 800 Mpc away from an observer have an average density equal to twice the cosmic mean. Unlikely as it is, having a region 40 - 300 Mpc away at half the cosmic mean density is still far more likely, albeit excluded at 6.04 sigma as shown in our work.

Regarding our proposed solution invoking Milgromian dynamics, this certainly does contain free parameters, more so than LCDM. It is certainly not a parameter-free description of cosmology, especially given that of course it does not uniquely predict that we should be in a KBC-like void. We could also have been living in an overdensity. What the model does is enhance cosmic variance sufficiently to allow us to live in a KBC-like void, with higher apparent local Hubble constant. The paper discusses why despite a wide range of possible theoretical assumptions, MOND should enhance cosmic variance enough to remove the Hubble tension, simply by increasing the error bars. After all, while a 6 sigma density fluctuation sounds very problematic for LCDM, doubling the cosmic variance on a 300 Mpc scale solves the problem, at least if this can be done without causing more problems elsewhere. But as we know, MOND actually works much better than LCDM on galaxy scales, so it would probably work better on all scales. And the paper explains why early Universe constraints like the CMB and primordial nucleosynthesis should not be problematic in MOND.

The MOND model has more free parameters, and explains many more observations. Whether it is better overall is a subjective matter, though I would argue that if LCDM is falsified, it is not the right model. MOND may not be the solution, but neither is LCDM. Personally, I believe that the MOND model comes much closer to the truth and is greatly preferred over LCDM despite the extra free parameters, due to these extra parameters allowing us to explain a wealth of observations:

https://tritonstation.com/2020/10/23/big-trouble-in-a-deep-void/#comment-18044

The way I understand it, the main additional parameters in MOND are the acceleration scale, the magnitude of the departure from Newtonian dynamics at a0 (which sets the sharpness of the interpolating function, but is not relevant to the KBC void as this is in the deep-MOND limit, as explained in the article), and for this project, the initial size and underdensity of the KBC void at high redshift. The initial void profile turns out to have only a small effect on our results, as discussed in the article. Interestingly, the Keenan+ (2013) paper and its figure 11 (which I mentioned above) already shows that their reported underdensity is quite similar to what would be required to solve the Hubble tension, which was already known back then. Neither the local nor the early Universe determinations of the Hubble constant have altered since then (maybe by 0.1 km/s/Mpc, but not appreciably). However, the error budgets have fallen. So the Hubble tension has only become more serious over the last seven years.

I have read more about the KBC underdensity. Figure 11 of KBC's paper (ApJ, 775, 62) surely indicates an anomaly. However, I am still concerned by the lack of agreement about its nature. It is puzzling that there are two independent entries in Wikipedia about the local void, and they do not even make clear that they are talking about the same object. You say in a previous post that our galaxy is not at the center. Is it so? It is not clear from what I read.

For me, the shape of a void (or underdensity) is important as well. The probabillity of an underdensity only specified by its value and volume is indefinite; that is to say, you can get many voids if you allow some slack in their shape.

It would also be helpful to know if the void has been observed in other galaxy surveys and with what features. Actually, I suppose that I should be able to locate it in my SDSS-DR7 VL samples.

Thanks for the link to the discussion on ""Deep Void". The counting of parameters in MOND in your post here seems somewhat peculiar, with "the initial size and underdensity of the KBC void at high redshift" included. I suppose that the "void profile" is related to my question about its shape :-)

I have to say that I do not know how many parameters the LCDM model really has.

My question was regarding concordance LCDM cosmology. By this, I mean LCDM with Planck parameters, or in general parameters fixed to whatever is required for the model to match the cosmic microwave background (CMB) anisotropies. As far as I understand, this model does not have many free parameters at all, but also one cannot consider the CMB anisotropies to be a success of the model because it is calibrated this way.

Of course, there was irony in my statement. However, if I try to seriously count parameters, then I get in trouble. Reading what wise men have written, e.g., in "The cosmological parameters" section of the Particle Data Group review, I do not know how many to count; in principle, maybe just 5+2, but there are surely more. Not to mention that they do not concider in detail the bias factor (or factors?).

You say that your MOND solution has more parameters. How many more? Have you been able to do a proper counting?

Jose Gaite: the MOND model as a whole only has a couple of extra parameters - the acceleration threshold, and the logarithmic slope of the gravity law below it. With these two parameters fixed, galaxy rotation curves emerge naturally as one can set g = sqrt(a_0*g_N). Possibly a third parameter should be added governing the sharpness of the transition between the Newtonian and Milgromian regimes, but certainly no more than these three parameters are needed. As for applying MOND to the KBC void, this is of course not a unique prediction of MOND - we could have been in an overdensity, or an even deeper underdensity. So in that case, one needs to know the initial size and strength of the void, and the external field. Much like when fitting a galaxy in LCDM, one would need to know properties of the dark matter halo. These are not free parameters of the paradigm, but are parameters for that particular project. So I would argue that MOND as a whole has 2 (maybe 3) parameters, though the sharpness of the interpolating function is relevant only in a small number of situations where the accelerations are close to a_0 (like the wide binary test, MNRAS, 480, 2660). This is not important to the KBC void, as explained in our publication modelling this in MOND. Another 3 parameters are needed for that study, but these are not fundamental in MOND. Whether we explain enough observations to justify these parameters is subjective, but certainly we can't do so without doing something new. Other explanations besides MOND are welcome.

Have a look at

Preprint How does the quantum structure of electromagnetic waves desc...

Just thought I would share this blog post explaining our work on El Gordo:

https://darkmattercrisis.wordpress.com/2021/01/16/54-the-interacting-galaxy-cluster-el-gordo-a-massive-blow-to-%ce%bbcdm-cosmology/

I've given an answer before but will give an even simpler answer here.

No, present cosmology is not even closely consistent with the observed large-scale structures of the universe. The problem is with the Hubble distance formula which greatly limits the age of the universe. Change the formula including the Hubble constant to calculate a far older universe. A far older universe would be much more consistent with what is being observed.

Forrest Noble maybe an older universe would give more structure, which could help. The ages of the oldest stars and globular clusters set a lower limit, and conventionally it is thought that they formed shortly after the Big Bang - so the age should be only a little bit larger. If the Universe is much older than conventionally thought, structure would need to form much more slowly at first.

Dear Indranil Banik,

I agree based upon present theory, but I propose a far older universe but not one infinite in age. One in which it takes at least 50 billion years to form large galaxy cluster structures, in total contrast to present theory.

Recent ΛCDM constraints for the large scale structure of the Universe were obtained from anisotropic galaxy clustering measurement, this is the paper https://www.aanda.org/articles/aa/full_html/2020/01/aa36772-19/aa36772-19.html

A much older universe makes sense. If we add two more attributes to the description of the universe, then the description becomes consistent as an alternative to the big bang theory.

The first attribute is finiteness. The universe has a closed topology with an equivalence of displacement and rotation. This means that every displacement is equivalent to a rotation of the view on the universe. The radius of the rotation is always the same and the position and orientation of the axes is a unique function of the displacement vector.

The second attribute is energy recycling. All elementary electromagnetic and kinetic processes of particles, including photons, lead to extremely weak gravitational waves. It takes millions of years until macroscopic impacts of this energy loss become visible. But the incoherent gravitational waves pile up to a background of positive gravitational energy density. If the energy density of the background has reached a critical level, a reaction with the gravitational field around black holes begins. The gravitational field around and inside black holes has like every gravitational field a negative energy density. An energy difference above the threshold triggers an equalisation mechanism, which leads to an energy transfer from the background into all black holes in the universe. Finally, all black holes explode and emit neutrons. The neutrons decay to hydrogen and provide star fuel for a new cycle.