Equation of state of gravitational energy in open de Sitter?

[Vincentius]

TL;DR Summary

Gravitational energy in de Sitter has EoS w=-1 (cosmological constant) and w=-1/3 (curvature energy in open or closed de Sitter). Is this just gravitational radiation, and how does this accord with EoS of photon radiation w=1/3?

Hi,
Gravitational energy in de Sitter has equation of state w=-1 (cosmological constant) and w=-1/3 (curvature energy in open or closed de Sitter). Is this just gravitational radiation, and how does this accord with the equation of state of photon radiation w=1/3?

Does this mean that densities of massless particles can have quite different EoS?

Thanks for answering!

 

[Arman777]

and w=-1/3 (curvature energy in open or closed de Sitter).

Never heard such thing. Where did you read it from ?

 

[PeterDonis]

Gravitational energy in de Sitter has equation of state w=-1 (cosmological constant) and w=-1/3 (curvature energy in open or closed de Sitter).

Where are you getting this from? Please give a reference.

 

[Vincentius]

Ok, maybe the question is wrong and I am just misunderstanding this. Retry:

There is no matter energy in de Sitter (empty), but still there is energy (cosmological constant w=-1 and curvature energy w=-1/3). Correct?

Then, as I understood, this energy is gravitational energy, therefore is relativistic, i.e., gravitational radiation. Correct?

If so, why does it have 2 equation-of-states, and why different from photon energy density w=1/3?

So clearly I am wrong somewhere, but not sure where.

 

[Vincentius]

In my knowledge there's only cosmological constant in the de-Sitter Universe. Logically curvature cannot have an equation of state ($w=-1/3$). That does not make sense. Only particles or "fluid" type things can have EoS.

De Sitter spacetime can be open, flat or closed, i.e., of negative, zero or positive Gaussian curvature K, and Friedmann equation

H² = H_Λ² - Ka^-2 ∝ρ_Λ + ρ_k

In general ρ ∝ a^-3(1+w_ρ)

Curvature energy is represented by the density ρ_k ∝a^-2, therefore w_k = -1/3

 

[Vincentius]

The point I try to raise is not whether Λ or K are part of the fluid equation. These densities represent energy, indeed of geometrical origin rather than being a matter fluid, although they can be represented as fluid components with EoS. But, as I already mentioned, I understand these energy components represent gravitational energy in de Sitter, which I understand is relativistic, i.e., gravitational radiation. If it is radiation, then one could expect it to dilute and be redshifted like a photon fluid, which it doesn't. Photon redsfift is also a geometrical effect, so it seems these fundamentally different energy components must still have something in common. I hope someone can shine some light on this.

I may add that Misner-Sharp mass M represents the internal energy of a fluid in spherical symmetry, where this fluid is unspecified otherwise. This is also a purely geometrical mass: M=R/2G where R is the radius of the cosmological apparent horizon. M happens to equal the Schwarzschild mass. This suggests that energy relevant to cosmology is all geometrical, like in de Sitter. Still there may be an equivalent representation in terms of matter components like dust (not so likely) or photon radiation (much more likely). This is the background of my question.

 

[PeterDonis]

There is no matter energy in de Sitter (empty), but still there is energy (cosmological constant w=-1 and curvature energy w=-1/3). Correct?

No. If you use the $w$ notation, de Sitter spacetime has $w = -1$ for the cosmological constant and that's it.

I don't know where you are getting "curvature energy" with $w = 1/3$ from. You need to give some references for where you are learning this stuff.

De Sitter spacetime can be open, flat or closed

These are just different choices of coordinates. They do not change the energy content of the spacetime.

Curvature energy

Is not an energy in the sense you are using the term.

I understand these energy components represent gravitational energy in de Sitter, which I understand is relativistic, i.e., gravitational radiation.

There is no gravitational radiation in de Sitter spacetime.

Misner-Sharp mass

Is not an energy density and has nothing to do with $w$.

This is the background of my question.

It seems like you are confused, probably because whatever source you are getting this from is either pop science, or is stating things in a way you are having trouble understanding correctly so you are drawing mistaken inferences. It would help if you would give references.