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### [1003.4531] Manifestly Covariant Gauge-invariant Cosmologic

Posted: March 30 2010

### [1003.4531] Manifestly Covariant Gauge-invariant Cosmologic

Posted: March 30 2010
Hi Anze,
Actually, I am a bit confused myself as well. I only had a quick look at the paper, but my attention fell on eqs (56) and (57) that describe the evolution of perturbations of the energy density $$\delta$$ in the "new" case and the standard case respectively.

There is clearly a huge difference in these two eqs and (if I understood it correctly - see Section I.B) the reason they give is that the pressure should depend both on the number n and the energy density $$\epsilon$$, ie $$p=p(n,\epsilon)$$, as they claim the perturbations actually do not evolve adiabatically. They explain why they believe this is so in a previous paper 0805.0421, see text near eq. (193)/page 30. Their result is that only in the non-relativist limit do the perturbations evolve adiabatically.

I might have missed or misunderstood something, but this is what I got after having a quick look. I can't say I am really convinced but I might have a closer look.

Cheers,
Savvas

PS By the way, the previous paper 0805.0421, doesn't seem to be published anywhere yet. I'm not sure about what this means.

### [1003.4531] Manifestly Covariant Gauge-invariant Cosmologic

Posted: March 31 2010
My understanding is that adiabaticity is an initial condition. I guess from a cursory look, assuming the math is correct, what they are effectively doing is evolving a mixture of curvature and entropy perturbations ...

### [1003.4531] Manifestly Covariant Gauge-invariant Cosmologica

Posted: April 01 2010
Hi Anze, Rishi and Savas,

The fact that density perturbations do evolve diabatically follows from $$p=p(n, \varepsilon)$$, thermodynamics (23) and the background Einstein equations (5).

The difference between (56) and (57) is that the general solution of the standard equation (57) contains the gauge function $$\psi$$. Consequently, the standard equation (57) has no physical meaning. The general solution of (56) is gauge-invariant, and $$\delta_\varepsilon$$ is the real, physical density contrast, as has been shown in Section IX on the non-relativistic limit. Note that in the large-scale limit, (56) yields the two well-known solutions proportional to $$t^{2/3}$$ and $$t^{-5/3}$$: see references below (45).

Regards,
Pieter

### [1003.4531] Manifestly Covariant Gauge-invariant Cosmologic

Posted: May 30 2010
Hi Anze, Rishi and Savvas,

I have just uploaded a new version. It will appear on arXiv June, 1.

I have added equations (26) and (27) for a better explanation why density perturbations in an expanding universe evolve diabatically.

If you have any further questions, please do not hesitate to contact me.

Cheers,
Pieter