A Models without dark energy

[phyzguy]

Several years ago, I posted about this paper, which claimed to be able to eliminate the need for dark energy by performing cosmological simulations differently, basically intercnaging the order of calculating the expansion rate and the average density. One quote from that paper is, "The algorithm exchanges the order of averaging and calculating the expansion rate and, due to the non-linearity of the equations, the two operations do not commute." They also claimed that this reduced the observed Hubble tension.

Now there are several reports in the popular science channels, like this one from phys.org, again saying there is no need for dark energy. This is based on this paper in MNRAS, which was based on this earlier work from Wiltshire.

What I think all of these papers are saying is that as the universe evolves, a larger and larger fraction of the universe volume is taken up by voids which are nearly devoid of matter. These voids expand faster (because of the lack of matter), and this is what is driving the accelerated expansion rate.

To me these arguments are very persuasive, and I would like to hear others' opinions and thoughts.

 

[PeroK]

Now there are several reports in the popular science channels, like this one from phys.org,

You should know this is not a valid reference.

To me these arguments are very persuasive, and I would like to hear others' opinions and thoughts.

What makes them very persuasive?

 

[Ibix]

The idea of trying to explain new phenomena without introducing new entities is always a good one, and whether small(ish) scale inhomogeneity changes things significantly from an FLRW solution is a question that had occurred to me (although not in this context). So on a personal level I like this approach and think it's worth investigating - but the question is if it really works. Apparently the newer paper linked in the OP says yes, but I guess time will tell.

I'll see if I can make sense of the papers.

 

[javisot20]

Cosmologists have done a lot of work according to the cosmological principle, it is reasonable to explore its negation. Carrying out this exploration and discovering that denying the principle can eliminate dark energy does not imply that this work is physically correct, but theoretically it is interesting.

 

[phyzguy]

You should know this is not a valid reference.

Of course it is not a valid reference, which is why I linked the actual paper the popular link was based on. I suspect that I am not alone in seeing many links saying that "scientists" are saying there is no need for dark energy, and I thought people might appreciate seeing some of the science behind it.

 

[phyzguy]

What makes them very persuasive?

If dark energy is really not needed, that would be a major step forward. The idea is simple, as I said. The voids expand faster than regions with matter, and by calculating the expansion rate from the average matter density, we are making an error. The first paper did a detailed simulation assuming different regions expand at different rates, and came up with results that match Lambda-CDM without the need for Lambda.

 

[phyzguy]

...whether small(ish) scale inhomogeneity changes things significantly from an FLRW solution...

"smallish scale inhomogeneities"? The cosmic voids are 100's of Mpc across, and the mass density in the voids is 10% of the average mass density or less. How is this smallish scale?

 

[PeroK]

If dark energy is really not needed, that would be a major step forward. The idea is simple, as I said. The voids expand faster than regions with matter, and by calculating the expansion rate from the average matter density, we are making an error. The first paper did a detailed simulation assuming different regions expand at different rates, and came up with results that match Lambda-CDM without the need for Lambda.

It would be good if you were able to summarise Wiltshire's approach and how it differs from the standard Friedmann equation. In standard cosmology, you cannot consider the regions separately, because the model applies to the universe as a whole.

"smallish scale inhomogeneities"? The cosmic voids are 100's of Mpc across, and the mass density in the voids is 10% of the average mass density or less. How is this smallish scale?

The standard model assumes that, on the largest scale, the galaxy clusters are evenly distributed. With that assumption, the Friedmann equation should be valid. That's why it would be interesting to understand why the Friedmann equation fails.

Without dark energy, as I'm sure you know, the expansion rate of a vacuum-dominated universe should be slowing down. If you take dark energy out of the equation, then the Friedmann equation would have to be very wrong.

That said, the key is how Wiltshire is able to calculate the expansion rate for voids in isolation.

 

[javisot20]

The standard model assumes that, on the largest scale, the galaxy clusters are evenly distributed. With that assumption, the Friedmann equation should be valid. That's why it would be interesting to understand why the Friedmann equation fails.

Without dark energy, as I'm sure you know, the expansion rate of a vacuum-dominated universe should be slowing down. If you take dark energy out of the equation, then the Friedmann equation would have to be very wrong.

What I was understanding (and maybe I'm wrong) is that standard cosmology is not invalidated. Standard cosmology would continue to be a good approximation in part of the life of the universe, but according to this work a poor approximation for all life of the universe. Dark energy is not "eliminated", it is "replaced", we continue to observe galaxies that seem governed by dark energy or this new analytical point of view.

From Wiltshire's earlier work,
"In general, the question of how to synchronize clocks in the absence of the exact symmetry described by a timelike Killing vector in general relativity does not have a solution, and the definition of quasilocal gravitational energy depends on choices of the splitting of spacetime into spatial hypersurfaces, the threading of
those hypersurfaces by observers, and the associated choice of surfaces of integration. Such choices are in general non-covariant and non-unique. One is essentially reduced to asking which choices of frame have the greatest physical utility. Since the ambiguities have their origin in the equivalence principle, my view is that the equivalence principle should be properly formulated and respected in the relative calibration of average frames in cosmology. I have therefore extended the strong equivalence principle as a cosmological equivalence principle (Wiltshire,2008) to apply to average spatially flat regions - cosmological inertial frames –undergoing a regionally homogeneous isotropic volume expansion with deceleration over arbitrarily long time intervals."

 

[ChemAir]

Wiltshire's (et. al.) more current work. I apologize if this has been posted somewhere else

December 2024 popsci article

Reference from that article
https://academic.oup.com/mnrasl/article/537/1/L55/7926647?login=false

 

[PeterDonis]

The standard model assumes that, on the largest scale, the galaxy clusters are evenly distributed.

Yes.

With that assumption, the Friedmann equation should be valid.

Not exactly, no. It is only an approximation, because constant density everywhere on a spacelike slice of constant FRW coordinate time is only an approximation. The question is how good an approximation.

The standard model assumes that the approximation is good enough. The alternate models being discussed here explore the possibility that it is not.

I haven't had a chance to read through any of the references in detail, but I don't think the possibility that the approximation is not good enough can just be dismissed out of hand.

 

[PeterDonis]

Dark energy is not "eliminated", it is "replaced"

I don't think this is a good description. Dark energy in the standard cosmological model is a component of the stress-energy of the universe that looks like a cosmological constant. In the alternate models under discussion in this thread, there is no component of the stress-energy of the universe that looks like a cosmological constant. That means dark energy is indeed eliminated. The observations that in the standard model are taken to show the presence of dark energy are accounted for in the alternate models by modeling the dynamics differently from the standard Friedmann equation.

 

[PeroK]

The standard model assumes that the approximation is good enough. The alternate models being discussed here explore the possibility that it is not.

I haven't had a chance to read through any of the references in detail, but I don't think the possibility that the approximation is not good enough can just be dismissed out of hand.

I was hoping to understand why the OP found the arguments "very persuasive". I looked at the last paper referenced. It was beyond my knowldege, but it looked like it was questioning the statistical basis of the expansion data.

 

[PeroK]

What I think all of these papers are saying is that as the universe evolves, a larger and larger fraction of the universe volume is taken up by voids which are nearly devoid of matter. These voids expand faster (because of the lack of matter), and this is what is driving the accelerated expansion rate.

This sounds like a description of the standard model, with dark energy. The papers, as far as I can tell, are concerned with a different statistical analysis of the data - although it doesn't say explicitly that the data then fits a non-accelerating expansion. If the conclusion is that there is no dark energy, then I'd assume we are left with a non-accelerating expansion?

That may be my misunderstanding.

 

[PeterDonis]

This sounds like a description of the standard model, with dark energy.

Not to me. A standard model with dark energy has the same expansion rate everywhere in space, and the expansion is accelerating due to dark energy. The alternate model being described does not have the same expansion rate everywhere in space, and the expansion is not accelerating--there is no dark energy (no component of the stress-energy that looks like a cosmological constant).

Again, I haven't yet had time to look through the papers in detail to see how they arrive at the claim that their alternate model can account for observations as well as standard Lambda CDM. But it seems clear to me that the alternate model is significantly different from standard Lambda CDM.

 

[PeterDonis]

a different statistical analysis of the data

To me, having only briefly skimmed the papers, looking at different ways of doing statistical analysis of the supernova data seems misplaced. What I would be looking for is a formulation of the alternate model from first principles, then using it to derive predictions for what the supernova data should look like, and comparing those predictions with the data--and then putting that comparison alongside the standard comparison of Lambda CDM with the data, to look at their respective fits. The Wiltshire paper might be more along these lines than the Seifert et al paper.

 

[Ibix]

The Wiltshire paper might be more along these lines than the Seifert et al paper.

I haven't had as much of a chance to read as I was hoping today, but I think so, yes. You may need to read earlier work of his, referenced in the last paper in the OP.

 

[PeroK]

To me, having only briefly skimmed the papers, looking at different ways of doing statistical analysis of the supernova data seems misplaced. What I would be looking for is a formulation of the alternate model from first principles, then using it to derive predictions for what the supernova data should look like, and comparing those predictions with the data--and then putting that comparison alongside the standard comparison of Lambda CDM with the data, to look at their respective fits. The Wiltshire paper might be more along these lines than the Seifert et al paper.

Yes, as far as I can follow the papers, that's my understanding.

 

[PeroK]

It might be worth noting that originally the case for an accelerating expansion was a surprise. A lot of time and effort must have been spent trying to get the emerging data to fit the model of non-accelerating expansion. Eventually, those efforts must have been abandoned and the case for an accelerating expansion accepted. And, the theoretically simplest solution was to add dark energy (aka Lambda) to the model.

It's not the case that dark energy was in the model from the start and data was massaged to fit an a priori expectation of accelerated expansion. Quite the reverse, in fact.

 

[phyzguy]

Not to me. A standard model with dark energy has the same expansion rate everywhere in space, and the expansion is accelerating due to dark energy. The alternate model being described does not have the same expansion rate everywhere in space, and the expansion is not accelerating--there is no dark energy (no component of the stress-energy that looks like a cosmological constant).

Exactly, that is my understanding as well. I think what is being claimed is that the approximation of the standard model that the acceleration is the same everywhere in space is incorrect. Regions of lower density expand faster and regions of higher density expand slower. The overall averaged expansion rate is accelerating because the regions of lower density are constituting a larger and larger fraction of the volume of the universe as time goes on.

 

[javisot20]

I don't think this is a good description. Dark energy in the standard cosmological model is a component of the stress-energy of the universe that looks like a cosmological constant. In the alternate models under discussion in this thread, there is no component of the stress-energy of the universe that looks like a cosmological constant. That means dark energy is indeed eliminated. The observations that in the standard model are taken to show the presence of dark energy are accounted for in the alternate models by modeling the dynamics differently from the standard Friedmann equation.

What differentiates Wiltshire's proposal from a proposal in which dark energy is not the cosmological constant?, I mean, can there be a model with variable dark energy that is the same as the Wiltshire model?

 

[PeterDonis]

What differentiates Wiltshire's proposal from a proposal in which dark energy is not the cosmological constant?

I didn't say dark energy is the cosmological constant, I said it looks like a cosmological constant. That's the definition of dark energy. If there is no stress-energy component that looks like a cosmological constant, which there isn't in Wiltshire's model, then there is no dark energy in the model, and that is what differentiates his proposal from a dark energy model.

 

[phyzguy]

What differentiates Wiltshire's proposal from a proposal in which dark energy is not the cosmological constant?, I mean, can there be a model with variable dark energy that is the same as the Wiltshire model?

In these proposals there is no dark energy of any type. The accelerated expansion comes from a reinterpretation of how to solve the equations of GR for an inhomogeneous universe.

 

[PeterDonis]

The accelerated expansion

I think one has to be careful here. As far as I can tell (I have not read the papers thoroughly), there is no actual accelerated expansion in the alternate model. There are different expansion rates in different parts of space (at a very heuristic level), but all of those expansions are decelerating--just not decelerating at the same rates (because the deceleration in a given region depends on the matter density--higher matter density, more deceleration, lower matter density, less deceleration). This makes sense because, if there is no dark energy, there is no way to have any accelerated expansion. That is still a consequence of the Einstein Field Equation, even in a model that is inhomogeneous.

 

[PeroK]

In these proposals there is no dark energy of any type. The accelerated expansion comes from a reinterpretation of how to solve the equations of GR for an inhomogeneous universe.

It would be helpful if you could show where Wiltshire indicates accelerated expansion. His "timescape" model, as far as I understand it, suggests that the data fits an empirical model where different regions are expanding at different rates due to the history of density variations. And that these local variations account for the apparent increase in expansion rate over time.

I don't believe that he presents an alternative solution to the field equations involving a general accelerating expansion. Can you reference where he does this?

The apparent accelerating expansion rate is attributed statistically and empirically to regional variations in expansion rate.

I'm happy to be corrected on this.

 

[Ibix]

I think what I'm getting from the paper is that you can see the density variation as inducing gravitational time dilation between a clock in a void and one in a dense region. Since the density differential grows with time the locally measured Hubble constant begins to differ from the global average and, in the case of observers in dense regions, this causes an apparent acceleration. Wiltshire is careful to note that this explanation is non-covariant, since this is very much not a stationary spacetime and you can't define gravitational potential in a covariant way. He also points out that if this explanation is correct the measured Hubble constant will depend on scale. At scales below the size of a dense region measurements are unaffected by relative time dilation and at very very large scales you measure more or less the average expansion, but in between you can come up with quite different values.

Wiltshire relies on equations he attributes to Buchert, which I haven't followed up. They appear to be the Friedman equations modified for a non-uniform universe.

 

[javisot20]

I don't believe that he presents an alternative solution to the field equations involving a general accelerating expansion. Can you reference where he does this?

"On the other hand, for samples strongly weighted by SNe Ia in the calibration regime of the ΛCDM model (𝑧CMB ≈ 0.04) there is no significant preference either way, the two models (timescape and LCDM) being statistically equivalent."

What they claim is that LCDM with accelerated expansion is statistically equivalent under certain conditions to the Timescape model. So Timescape, which does not contain accelerated expansion, could explain the same thing under those conditions as LCDM, with accelerated expansion. Where the effects of inhomogeneity begin to be cosmologically relevant, the timescape model is prioritized.(according to the authors)


I add the work of T. Buchert that contains the equations on which Wiltshire is based, https://arxiv.org/abs/gr-qc/9906015
https://arxiv.org/abs/1912.04213

 

[PeroK]

"On the other hand, for samples strongly weighted by SNe Ia in the calibration regime of the ΛCDM model (𝑧CMB ≈ 0.04) there is no significant preference either way, the two models (timescape and LCDM) being statistically equivalent."

What they claim is that LCDM with accelerated expansion is statistically equivalent under certain conditions to the Timescape model. So Timescape, which does not contain accelerated expansion, could explain the same thing under those conditions as LCDM, with accelerated expansion. Where the effects of inhomogeneity begin to be cosmologically relevant, the timescape model is prioritized.(according to the authors)

I assume, however, that they cannot remain statistically equivalent indefinitely. A billion more years of universal evolution would resolve the matter?

 

[javisot20]

I assume, however, that they cannot remain statistically equivalent indefinitely. A billion more years of universal evolution would resolve the matter?

Exactly, according to the authors when "the matter is resolved" it should be resolved in favor of the inhomogeneous cosmology of timescape (but they must check that it is not all a product of "massaging the data")

Using naïve language, we can assume that voids are not a problem at the beginning of the universe, but it will evolve and become a problem

 

[ThickTarget]

The idea isn't really so simple under the surface. The debate in this (sub)field is whether this inhomogeneous expansion (backreaction) exists even in theory. GR is sufficiently complicated that it can only be solved exactly in a few cases. In the standard treatment, one averages the inhomogeneities to get a global solution, and then treat the growth of structures on top of this background cosmology. Proponents of backreaction believe that some important physics is missed in this process, and it was conjectured that this might explain dark energy, but thus far they have been unable to prove it is possible. In opposition there were (e.g.) the Green and Wald papers, and the Newtonian approximation there is zero backreaction. Backreaction is a fringe topic within cosmology, and the standard interpretation is that it is negligible or zero.

https://arxiv.org/abs/1703.08809

To me, it is more than a bit premature to look at one cosmological test in isolation and declare there is need for paradigm shift. The road to showing this is even a viable model is much longer, one needs to look at all the data simultaneously. Another point is that this model was created to explain dark energy, so it's not really surprising that it can fit the supernovae data. They have traded one parameter (Lambda) for their void parameter. If they could calculate the strength of dark energy purely from cosmic structure and their model, that would be impressive, but they are fitting it. If one wants to really demonstrate that this inhomogeneous expansion really exists in the real universe then there needs to be some novel observational test for that, I'm aware of one such paper which found no signal. It doesn't disprove the whole idea, but it's an example of a novel paradigm test.

https://arxiv.org/abs/1811.11976