The effective equation of state in Rastall gravity.

In this paper, we study a homogeneous and isotropic flat Friedmann–Robertson–Walker (FRW) universe in Rastall gravity, in which there exist the components of radiation and dust. That is to say, the density of fluid ρ γ satisfies the barotropic equation of state p γ = (γ − 1) ρ γ , where γ = 4 / 3 and 1 , and the equation of state w = γ − 1. We derive the modified Friedmann equations, and the effective equation of state w ̃ in this universe model. For the dust-dominated case, the effective equation of state w ̃ is described by λ − 1 3 λ − 1 , where λ is the Rastall parameter. As 1 3 < λ < 2 3 , we have w ̃ < − 1 3 which means an accelerated expansion of the universe occurs. Along with the conditions for the convergent modified Friedmann equations and the positive density of dust, the Rastall parameter λ should be in the range of (1 2 , 2 3). In other words, the various w ̃ for 1 2 < λ < 2 3 correspond to those of quintessence with the general barotropic equation of state (γ = 1). For the general case, the Rastall universe full of radiation and dust, the expression of w ̃ is complicated involving the Rastall parameter, the density of radiation and the density of dust. As the ratio of the densities of dust and radiation is smaller than 2 − 3 λ 2 (2 λ − 1) , w ̃ is less than − 1 3 . Moreover, to keep the density of dust positive, the Rastall parameter should be restricted in (1 2 , 2 3) too. By the numerical calculation, we find that w ̃ from 1 3 decreases as N (N ≡ l n a (t)) increases. And w ̃ for different λ ∈ (1 2 , 2 3) ultimately tend to λ − 1 3 λ − 1 , the value of which are in the range of (− 1 , − 1 3). Obviously, the expansion of the cosmology filled with radiation and dust or only dust in Rastall gravity (1 2 < λ < 2 3) accelerates without any "exotic" energy whose equation of state w < − 1 3 . [ABSTRACT FROM AUTHOR]