
CosmoCoffee

[1003.4531]
Manifestly Covariant Gaugeinvariant Cosmological Perturbation Theory

Authors:  P. G. Miedema, W. A. van Leeuwen 
Abstract:  It is shown that a firstorder cosmological perturbation theory for the open,
flat and closed FriedmannLemaitreRobertsonWalker universes admits one, and
only one, gaugeinvariant variable which describes the perturbation to the
energy density and which becomes equal to the usual Newtonian energy density in
the nonrelativistic limit. The same holds true for the perturbation to the
particle number density. Using these two new variables, a new manifestly
gaugeinvariant cosmological perturbation theory has been developed. Density
perturbations evolve diabatically. Perturbations in the total energy density
are gravitationally coupled to perturbations in the particle number density,
irrespective of the nature of the particles. There is, in firstorder, no
backreaction of perturbations to the global expansion of the universe.
Smallscale perturbations in the radiationdominated era oscillate with an
increasing amplitude, whereas in older, less precise treatments, oscillating
perturbations are found with a decreasing amplitude. This is a completely new
and, obviously, important result, since it makes it possible to explain and
understand the formation of massive stars after decoupling of matter and
radiation. 

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Anze Slosar
Joined: 24 Sep 2004 Posts: 205 Affiliation: Brookhaven National Laboratory

Posted: March 30 2010 


Could someone who knows better tell me if I should read/worry about this paper or not? 

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Savvas Nesseris
Joined: 05 Apr 2005 Posts: 68 Affiliation: UAM/IFT

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 δ 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 ε, ie p = p(n,ε), 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 nonrelativist 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. 

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rishi khatri
Joined: 23 Dec 2009 Posts: 6 Affiliation: Tata Institute of Fundamental Research

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 ... 

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Pieter Miedema
Joined: 18 May 2008 Posts: 2 Affiliation: Netherlands Defence Academy

Posted: April 01 2010 


Hi Anze, Rishi and Savas,
Thank you for your comments on my article.
The fact that density perturbations do evolve diabatically follows from , 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 ψ. Consequently, the standard equation (57) has no physical meaning. The general solution of (56) is gaugeinvariant, and is the real, physical density contrast, as has been shown in Section IX on the nonrelativistic limit. Note that in the largescale limit, (56) yields the two wellknown solutions proportional to t^{2 / 3} and t^{ − 5 / 3}: see references below (45).
Regards,
Pieter 

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Pieter Miedema
Joined: 18 May 2008 Posts: 2 Affiliation: Netherlands Defence Academy

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 

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