A note on non-vanishing divergence of the stress-energy tensor in theories of gravity

Abstract

In this paper we investigate three theories characterised by non-vanishing divergence of the stress-energy tensor, namely f (R, LM ), f (R, T ), and Rastall theory. We show that it is not possible to obtain the third from the first two, unless in some very specific case. Nonetheless, we show that in the framework of cosmology in the f (R, T ) theory, a result similar to that found in the Rastall one is reproduced, namely that the dynamics of the ΛCDM model of standard cosmology can be exactly mimicked, even though the dark energy component is able to cluster.

Cosmic dynamics and qualitative study of Rastall model with spatial curvature

“…On the physical grounds in cosmological modeling, a functional dependence of energy density on the pressure of the model may be postulated. We consider a perfect fluid with affine equation of state having form [26] p = αρ − ρ 0 (11) here α, ρ 0 are free parameters. This affine equation of state (EoS) provides the description of both hydrodynamically unstable (α < 0) and stable (α > 0) fluids.…”

“…The difficulty of Rastall's proposal is that the field equations are taken without any Lagrangian formulation. There have been various attempts for the Lagrangian formulation of Rastall theory in literature [8][9][10][11]. Fabris et al [11] have demonstrated that there is a way to cast the Ratall gravity theory with f (R, T ) theory [12] is by the hydrodynamical representation of a scalar field.…”

“…There have been various attempts for the Lagrangian formulation of Rastall theory in literature [8][9][10][11]. Fabris et al [11] have demonstrated that there is a way to cast the Ratall gravity theory with f (R, T ) theory [12] is by the hydrodynamical representation of a scalar field. Rastall's theory provides a setting in which energy-momentum sources and geometry can be non-minimally coupled to each other.…”

“…The energy density of the universe during inflation may be drawn from the negative energy of the gravitational source field [13,14]. Various theoretical and observational features of Rastall theory have been studied in literature [3,6,7,[9][10][11][15][16][17][18][19][20][21][22][23]. In response to Visser's claim that the Rastall gravity is completely equivalent to General Relativity [24], Darabi et al [20] have illustrated that Rastall gravity is a form of modified gravity different from General relativity.…”

Cosmological implications of Rastall-$f(R)$ theory

“…One of the important debates on the Rastall idea is to construct a fully covariant action which leads to the Rastall equations of motion. For example a relationship between Rastall theory and f (R, L m ) theory is considered in [26] where the authors constraint the Rastall parameter to lie in the range λ ≤ 0 and λ ≥ 1 using energy conditions. Also, the relation between Rastall theory and k-essence model is considered in [27] where the authors claimed that both theories produce same solutions.…”