3 fates of universe holds for which cosmological fluids?

[binbagsss]

I’ve read that most comoglocial fluids can be modeled as perfect fluids. And that most perfect fluids obey $p=w/rho$.

I’m wondering (had a look around and can’t seem to find) two things:
i) whenever $p=w/rho$ is obeyed does this always give the 3 descriptions of the universe – 2 open universes expanding at different rates and one closed universe
ii) examples of cosmological fluids which do not obey $p=w/rho$? And do these fluids still lead to the same 3 fates of the universe. Does any perfect fluid lead to these 3 universes?

Thanks in advance.

I'm new to this and my question is motivated by taking the single case of a couple of fluids, with different w values, which do obey the above equation of state and looking at friedmann equations and finding that it leads to the 3 desriptions of the universe. I'm now wondering how well this generalises - to finidng the same 3 universe fates.

 

[PeterDonis]

First of all, your cosmological equation of state is wrong: it should be $w = p / \rho$, or $p = w \rho$. See here:

http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

A perfect fluid does not have to have an equation of state of this general form, but all of the ones used in cosmological models do.

The most general model of a cosmological fluid would allow for a combination of different components with different values of $w$. However, in practice, the dynamics of the universe at any particular epoch is dominated by one component, i.e., by one particular value of $w$. For example, during the inflationary era, the universe was dominated by the inflaton field, with $w = -1$ (at least, as best we can tell); then, after inflation ended, there was a radiation-dominated period ($w = 1/3$), for about 100,000 years; then there was a matter-dominated period ($w = 0$) up until a few bilion years ago; and now the dynamics is dark energy-dominated ($w = -1$, as best we can tell).

The fate of the universe is governed by the value of $w$ which dominates in the far future (as best we can tell, this will be dark energy in our actual universe) and by the spatial curvature (closed, flat, or open). Note that the spatial curvature is an input to the model; the model doesn't tell us what it is, so we have to obtain it by measurements (as best we can tell with our current measurements, our universe is spatially flat). The combination of the spatial curvature and the value of $w$ determines whether the universe will expand forever or recollapse in a Big Crunch.

 

[binbagsss]

A perfect fluid does not have to have an equation of state of this general form, but all of the ones used in cosmological models do.

Sorry to re-bump an old thread but is it that he comsological fluids are perfect fluids,or are they approximated by a perfect fluid? thanks.

 

[PeterDonis]

is it that he comsological fluids are perfect fluids,or are they approximated by a perfect fluid?

If you mean, is the actual matter and radiation in the universe a perfect fluid, obviously not. Modeling the matter and radiation as a perfect fluid is an approximation that is only valid on large distance scales.

Modeling the dark energy as a perfect fluid is a much better approximation, because as far as we can tell its density is constant even on very small distance scales. However, that doesn't mean it actually "is" a perfect fluid or a very good approximation to one, in the sense that, say, air is. It's just that modeling it as a perfect fluid with a $w = -1$ equation of state works very well.