The effective equation of state in Rastall gravity

Abstract

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 [Formula: see text] satisfies the barotropic equation of state [Formula: see text], where [Formula: see text] and [Formula: see text], and the equation of state [Formula: see text]. We derive the modified Friedmann equations, and the effective equation of state [Formula: see text] in this universe model. For the dust-dominated case, the effective equation of state [Formula: see text] is described by [Formula: see text], where [Formula: see text] is the Rastall parameter. As [Formula: see text], we have [Formula: see text] 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 [Formula: see text] should be in the range of [Formula: see text]. In other words, the various [Formula: see text] for [Formula: see text] correspond to those of quintessence with the general barotropic equation of state [Formula: see text]. For the general case, the Rastall universe full of radiation and dust, the expression of [Formula: see text] 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 [Formula: see text], [Formula: see text] is less than [Formula: see text]. Moreover, to keep the density of dust positive, the Rastall parameter should be restricted in [Formula: see text] too. By the numerical calculation, we find that [Formula: see text] from [Formula: see text] decreases as [Formula: see text] increases. And [Formula: see text] for different [Formula: see text] ultimately tend to [Formula: see text], the value of which are in the range of [Formula: see text]. Obviously, the expansion of the cosmology filled with radiation and dust or only dust in Rastall gravity [Formula: see text] accelerates without any “exotic” energy whose equation of state [Formula: see text].