Why isn't back-reaction receiving more study?

[phyzguy]

TL;DR Summary

The idea that backreaction (the effect of inhomogeneities in matter and geometry on average cosmic evolution) is the source for the apparent late-time accelerated expansion of the Universe is known as the backreaction conjecture.

This paper on the arXiv today is another discussion of backreaction in cosmology. The idea here is that when we assume an FLRW metric, which is homogeneous and isotropic, we are making a significant error. We know the universe is not homogeneous; there are dense regions and large low-density cosmic voids. Since the low density regions expand more rapidly (because there is less matter in them), this can lead to an accelerated expansion that mimics the effects of dark energy. I am reminded of this paper, where they did an N-body simulation taking these inhomogeneities into account, and found that (1) there is no need for dark energy, and (2) it can explain the observed Hubble constant discrepancy. In the first paper above, they say, "At this point, it is still up for debate to what extent cosmic backreaction is important in the real universe." I continue to find this model compelling and would like to hear comments from others on this forum.

By the way, the point of the first paper above is that better observations in the next few decades, especially of red-shift drift (which is the measurement of the change of redshift with time of a particular object) will be able to confirm or deny the backreaction hypothesis.

 

[trurle]

Currently used Lambda-CDM model is the model with the minimal amount of parameters explaining all current observations.
Backreaction models do introduce additional, difficult to model parameters (distribution of ordinary matter) , and therefore most physicists dislike backreaction models - at least until it will be experimentally proven what lambda-CDM model is inadequate.

 

[ohwilleke]

I would somewhat question the premise that this theory is getting "too little" attention because it isn't easy to set a baseline of what is "a lot of attention" and it does have a number of papers written about it by multiple independent groups of researchers.

 

[phyzguy]

A would somewhat question the premise that this theory is getting "too little" attention because it isn't easy to set a baseline of what is "a lot of attention" and it does have a number of papers written about it by multiple independent groups of researchers.

Thanks for that. If you know of any good papers, especially review articles, please post some references.

 

[Heikki Tuuri]

https://arxiv.org/abs/1505.07800

https://arxiv.org/abs/1506.06452

The camp of Green and Wald fought against the camp of T. Buchert over the importance of the backreaction, around 2015.

They could not agree on anything.

Note that there is no proof that the Einstein equations have any solution with a nonuniform matter distribution. It might be that the importance of the backreaction has no correct answer at all.

 

[Orodruin]

Note that there is no proof that the Einstein equations have any solution with a nonuniform matter distribution. It might be that the importance of the backreaction has no correct answer at all.

Note that this is a mathematical question rather than a physical one. If no such solution exists then the physical implication would just be that the EFEs simply is not an accurate enough description of observations (because it would be inconsistent with observation) although the homogenous solutions and numerical solutions come pretty darn close.

 

[phyzguy]

We can solve the EFE numerically in cases with very nonuniform matter distributions - merging neutron stars for example. Why can't we use these numerical methods to model a universe which is initially FLRW with small perturbations? We could use linear theory to grow the initial perturbations up to some point, and then take over with a full numerical simulation of the EFE. Is the problem just numerically too large to be tractable? Does anyone know if this has been (or is being) tried?

 

[martinbn]

Note that there is no proof that the Einstein equations have any solution with a nonuniform matter distribution. It might be that the importance of the backreaction has no correct answer at all.

This as stated is not true. Perhaps i am missing the context.

 

[Heikki Tuuri]

We can solve the EFE numerically in cases with very nonuniform matter distributions - merging neutron stars for example. Why can't we use these numerical methods to model a universe which is initially FLRW with small perturbations? We could use linear theory to grow the initial perturbations up to some point, and then take over with a full numerical simulation of the EFE. Is the problem just numerically too large to be tractable? Does anyone know if this has been (or is being) tried?

The papers of Buchert et al. or Green et al. do not mention any numerical FLRW simulation with the Einstein equations, with nonuniform matter distribution.

I have understood that current simulations of galaxy formation assume the perfectly symmetric FLRW geometry and then use Newtonian gravity to calculate the lumping of the matter. They are hybrid models and not really General relativity models.

Merging neutron stars are modeled embedded into an asymptotic Minkowski space. Post-Newtonian calculations correct an initial Newtonian calculation.

Thus, current simulations work in a simple symmetric background geometry: Minkowski or FLRW.

There is one obvious problem in modeling the whole universe with a nonuniform matter distribution: what should be the initial geometry? It cannot be the perfectly symmetric FLRW. What should it be?

If there are no solutions of the Einstein equations with nonuniform matter, then it may be that all attempts to construct an initial geometry diverge.

What about measuring the current geometry empirically? Buchert et al. argue that it is very hard to measure it with enough precision.

 

[Heikki Tuuri]

This as stated is not true. Perhaps i am missing the context.

Please look at:

http://www.numdam.org/item/?id=SEDP_1989-1990____A15_0

No one in literature claims that the existence of solutions for a nonuniform mass distribution has been proved.

The situation is the same for many partial differential equations in physics. If you can prove the stability of the Navier-Stokes equation, you will receive a Clay Millennium prize.

 

[phyzguy]

There is one obvious problem in modeling the whole universe with a nonuniform matter distribution: what should be the initial geometry? It cannot be the perfectly symmetric FLRW. What should it be?

Why can't it be what I proposed earlier - a symmetric FLRW universe with a small density perturbation added on top? We know the initial density of the universe was quite uniform.

 

[PAllen]

Please look at:

http://www.numdam.org/item/?id=SEDP_1989-1990____A15_0

No one in literature claims that the existence of solutions for a nonuniform mass distribution has been proved.

The situation is the same for many partial differential equations in physics. If you can prove the stability of the Navier-Stokes equation, you will receive a Clay Millennium prize.

Stability is a completely different question from existence of solution. Simply take an arbitrary anisotropic inhomogenous metric in terms of some analytic functions, compute the Einstein tensor and thus the stress energy tensor, and you have a solution. Then, the physical question to analyze is the meaning and plausibility of the stress energy tensor. That then gets into unresolved questions about what is reasonable "filter" to define physical plausibility. At one time, the dominant energy condition was the gold standard, but that is no longer so. However, it is still unambiguously, rigorously, true that you can construct non-uniform solutions of the EFE. Again, stability is a separate question, and even whether stability is required is yet another separate question.

 

[Orodruin]

Why can't it be what I proposed earlier - a symmetric FLRW universe with a small density perturbation added on top? We know the initial density of the universe was quite uniform.

What you propose is a solution using approximative and numerical methods. Such solutions do not show that the solution to the differential equations actually exist in the mathematical sense.

 

[martinbn]

Please look at:

http://www.numdam.org/item/?id=SEDP_1989-1990____A15_0

No one in literature claims that the existence of solutions for a nonuniform mass distribution has been proved.

The situation is the same for many partial differential equations in physics. If you can prove the stability of the Navier-Stokes equation, you will receive a Clay Millennium prize.

None of this is correct.

The stability of Minkowski is irrelevant here. But even that shows that your claim is wrong. The theorem shows that any solution that is initially close to Minkowski remains close to Minkowski, no assumption about uniformity.

It is also not true about other differential equations. Why do you even think it might be the case!?

The Clay prize problem is about global regularity of Navier-Stokes not about stability.

 

[phyzguy]

What you propose is a solution using approximative and numerical methods. Such solutions do not show that the solution to the differential equations actually exist in the mathematical sense.

I wasn't arguing that point. To me these arguments about the existence of solutions seem somewhat silly. Numerical solutions to the EFEs accurately predict what we are observing in the case of merging black holes or merging neutron stars, so why not apply these same methods to the questions about cosmology? The arguments about stability of the Navier-Stokes equations don't stop people from doing computational fluid dynamics, which is a very successful field.

 

[PeterDonis]

Moderator's note: A number of off topic posts have been deleted.

 

[Orodruin]

I wasn't arguing that point. To me these arguments about the existence of solutions seem somewhat silly. Numerical solutions to the EFEs accurately predict what we are observing in the case of merging black holes or merging neutron stars, so why not apply these same methods to the questions about cosmology?

You may not have been intending to argue that point, but it is what the poster you replied to wanted. I agree that numerics and approximations are sufficient to give accurate predictions, I just think that was beside the point being made.

 

[Buzz Bloom]

I am wondering if any of the PFs community knows whether the question of finding a mathematical GR solution for an simple assumed non-isotropic universe has been investigated at all. An example of what I am asking is: assume the following as the initial conditions of a universe described by the Friedmann equation: flat and filled with dust and no dark energy (avoiding the radiation term and curvature turn and cosmological constant term), and also assume the dust is uniformly distributed except for one large spherical void. Has anyone explored how a simple non-isometric universe like this example universe evolves, and how does space-time vary with respect to distance from the void (based on some criteria for defining it).

My thought is that if such a solution is found, then it might provide some insight to the back-reaction concept.

If this post is determined to be off-topic, I will try to re-post it to start a new category-I thread.

 

[PAllen]

I am wondering if any of the PFs community knows whether the question of finding a mathematical GR solution for an simple assumed non-isotropic universe has been investigated at all. An example of what I am asking is: assume the following as the initial conditions of a universe described by the Friedmann equation: flat and filled with dust and no dark energy (avoiding the radiation term and curvature turn and cosmological constant term), and also assume the dust is uniformly distributed except for one large spherical void. Has anyone explored how a simple non-isometric universe like this example universe evolves, and how does space-time vary with respect to distance from the void (based on some criteria for defining it).

My thought is that if such a solution is found, then it might provide some insight to the back-reaction concept.

If this post is determined to be off-topic, I will try to re-post it to start a new category-I thread.

Giant voids were a hot research topic as an alternative to dark energy for a while. I haven't heard anything new on this in a while, so I'm thinking some mismatch with observation occurred. Hopefully, someone else here knows the history on this. @kimbyd, @Bandersnatch ?