Density fluctuations in a homogeneous linearly expanding universe?

[Suekdccia]

TL;DR

Density fluctuations compatible with a homogeneous and isotropic linearly expanding universe?

I would like to ask a question about an interesting paper [1] back from the late 90's

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 contrary to the classical view of heat death, in Big Bang cosmology the issue is more subtle as the temperature of the universe is continually changing, so a continually expanding universe would not really arrive to thermodynamic equilibrium and thus heat death as a whole (note that this paper was written a year before we discovered the accelerated expansion of the universe, so they mostly consider scenarios with a cosmological linear expansion)

However, if we consider local pockets or regions, the expansion can turn a comoving volume into an adiabatic one, 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 heat death wouldn't happen

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

The last case is an open universe: Here heat death 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 without definitive conclusions).

Once summarized, I have question about this paper which is the following one:

I think this argument, if you read V.B., is based on suggesting the local/observable density parameter being different from the density parameter on a larger scale. I would say this is not the standard assumption when thinking about questions like this, rather we assume global homogeneity. So how can these authors have overlooked that? How can this argument that the universe wouldn't reach heat death globally (or even locally if it was flat) be compatible with the assumption that the universe is globally homogeneous and isotropic?


[1]: https://arxiv.org/abs/astro-ph/9701131

 

[PeterDonis]

we assume global homogeneity

Not if we're considering density fluctuations, as this paper does. Obviously if you assume global homogeneity there are no density fluctuations, so if you want to analyze the effects of density fluctuations you can't assume global homogeneity.

 

[Suekdccia]

Not if we're considering density fluctuations, as this paper does. Obviously if you assume global homogeneity there are no density fluctuations, so if you want to analyze the effects of density fluctuations you can't assume global homogeneity.

Oh makes sense

Even then, the universe can have local density variations. Could the paper still be valid if we consider this? Or this would only work if the universe was globally inhomogeneous?

 

[PeterDonis]

the universe can have local density variations. Could the paper still be valid if we consider this? Or this would only work if the universe was globally inhomogeneous?

There is no such thing as "local density variations but globally homogeneous". Either the density is constant everywhere in space at an instant of FRW coordinate time or it isn't. The paper is considering the case where it isn't.

 

[Suekdccia]

There is no such thing as "local density variations but globally homogeneous". Either the density is constant everywhere in space at an instant of FRW coordinate time or it isn't. The paper is considering the case where it isn't.

Mmmh but at a local level, the density is not absolutely constant, is it? Galaxies are not separated by the exact same distance, some regions have overdensities of matter

 

[PeterDonis]

at a local level, the density is not absolutely constant, is it?

The FRW model of the universe is an approximation in which the density is treated as constant everywhere; any variations are ignored.

The paper you reference is using a different model in which density variations are not ignored.

 

[Suekdccia]

The FRW model of the universe is an approximation in which the density is treated as constant everywhere; any variations are ignored.

The paper you reference is using a different model in which density variations are not ignored.

Alright, understood

 

[timmdeeg]

TL;DR Summary: Density fluctuations compatible with a homogeneous and isotropic linearly expanding universe?

Why linearly expanding? This would require flat spacetime. In curved spacetime the universe expands either decelerated or accelerated, depending on its ingredients.