3 questions about a paper on density fluctuations in the Universe

[Suekdccia]

TL;DR Summary

3 questions about a paer: Are density perturbations possible in a globally homogeneous and isotropic universe? Can the local and large density be different in the indefinite future? Do density fluctuations become "frozen" in an open universe?

I would like to ask some questions about an interesting paper that was written back in the late 90's (https://arxiv.org/abs/astro-ph/9701131)

There, the authors propose how the universe may evolve from the near future to extremely far time scales

Near the end of it (Section VI, D.), they discuss entropy and heat death: They indicate that the temperature of the universe would be continually changing, so a continually expanding universe would not really ever arrive to a thermodynamic equilibrium.

However, if we consider local pockets or regions, the expansion can make that a comoving volume becomes adiabatic so at that local level entropy would reach a maximum value. So according to this paper, while global heat death would not be attained, local or "cosmological" heat death could occur

Then they consider the case for the different main possible geometries of the universe:

- If it's closed it would probably end up in a big crunch, so thermodynamic equilibrium wouldn't really happen

- If it's flat density perturbations of larger and larger scales could enter the horizon allowing the production of entropy so thermnodynamic equilibrium would be avoided even at that local level

- The last case is an open universe: Here thermodynamic equilibrium could happen as density fluctuations become "frozen" at a finite length scale (although they give some caveats i.e. that the Bekenstein bound does not directly constrain entropy production in this case, so actually is an open question).

Once summarized, my questions about this paper are the following ones:

1. It seems that this argument, considering section V.B., is based on suggesting the local/observable density parameter being different from the density parameter on a larger scale. But I think this is not the standard assumption when thinking about questions like this, rather we assume global homogeneity. So how can the authors' argument that the universe wouldn't reach thermodynamic equilibrium globally (or even locally if it was flat) be compatible with the assumption that the universe is globally homogeneous and isotropic? It is strange because early in the paper, they seem to be aware that the consensus was that the universe is globally homogeneous and isotropic (see page 34)... Is it because they are talking about small deviations from global homogeneity and isotropy that would be small enough to be compatible with our observations and models?

2. It’s not clear to me that the local density can be different from the large scale density infinitely far in the future. Is this possible?

3. I don't really understand why would density fluctuations become frozen in an open universe. Is it because they are considering an accelerated expanding universe with the existence of a cosmological constant/horizon in this case?

 

[PeterDonis]

Are density perturbations possible in a globally homogeneous and isotropic universe?

No, but that's irrelevant, because we know our universe is not exactly homogeneous and isotropic; it's only approximately so.

we assume global homogeneity

Not when we're considering density perturbations. When we do that, we are explicitly recognizing that global homogeneity is just an approximation, and we're investigating how much the actual universe might deviate from that approximation based on the data we have.

Is it because they are talking about small deviations from global homogeneity and isotropy that would be small enough to be compatible with our observations and models?

Obviously. See above.

It’s not clear to me that the local density can be different from the large scale density infinitely far in the future. Is this possible?

With the particular definitions the paper is using, yes. Basically they appear to be averaging over different distance scales.

I don't really understand why would density fluctuations become frozen in an open universe. Is it because they are considering an accelerated expanding universe with the existence of a cosmological constant/horizon in this case?

Not just that, no, because there is also a cosmological horizon in the flat case. The difference in the open case is that the cosmological horizon does not approach a constant size in terms of comoving distance; it keeps expanding, logarithmically. But the "speed of light sphere" (which looks like what is called the Hubble sphere in other sources) does approach a constant comoving distance. So, unlike the flat case, in the open case the Hubble sphere becomes smaller than the cosmological horizon. That is what "freezes" density fluctuations--or more precisely, what prevents density fluctuations from entering the cosmological horizon from outside after a certain time.