The matter in the Big-Bang model is dust and not any arbitrary perfect fluid!

Abstract

We consider a spherically symmetric general relativistic perfect fluid in its comoving frame. It is found that, by integrating the local energy momentum conservation equation, a general form of g ₀₀ can be obtained. During this study, we get a cue that an adiabatically evolving uniform density isolated sphere having ρ(r,t)=ρ ₀(t), should comprise “dust” having p ₀(t)=0; as recently suggested by Durgapal and Fuloria (J. Mod. Phys. 1:143, 2010) In fact, we offer here an independent proof to this effect. But much more importantly, we find that for the homogeneous and isotropic Friedmann-Robertson-Walker (FRW) metric having p(r,t)=p ₀(t) and ρ(r,t)=ρ ₀(t), $g_{00} = e^{-2p_{0}/(p_{0} +\rho_{0})}$. But in general relativity (GR), one can choose an arbitrary t→t _∗=f(t) without any loss of generality, and thus set g ₀₀(t _∗)=1. And since pressure is a scalar, this implies that p ₀(t _∗)=p ₀(t)=0 in the Big-Bang model based on the FRW metric. This result gets confirmed by the fact the homogeneous dust metric having p(r,t)=p ₀(t)=0 and ρ(r,t)=ρ ₀(t) and the FRW metric are exactly identical. In other words, both the cases correspond to the same Einstein tensor $G^{a}_{b}$ because they intrinsically have the same energy momentum tensor $T^{a}_{b}=\operatorname {diag}[\rho_{0}(t), 0,0, 0]$.