Non-minimal coupling inspires the Dirac cosmological model

Abstract

In the framework of the generalized Rastall theory (GRT), we study the ability of a non-minimal coupling between geometry and matter fields in order to provide a setting which allows for a variable G during the cosmic evolution. In this regard, the compatibility of this theory with Dirac hypothesis on the variations of G is investigated, and additionally, the possibility of obtaining the current accelerated universe is also addressed. In summary, our study indicates that, in GRT, having in hand the G profile, one may find the corresponding non-minimal coupling between the energy source and geometry and vise versa, in a compatible way with the current accelerated universe.

Dynamical systems of cosmological models for different possibilities of $G$ and $ρ_Λ$

“…where f 1 (x, y) = (α 2 − 3)x − (γ−1)y 8πG and g 1 (x, y) = −3γy. Using (27), the above equation becomes…”

“…In Newtonian gravity, without any requirement of further constraints to be satisfied we can explicitly write the time variation of G. But in GR there are other constraints to be satisfied. For instance if we assume that the ordinary energy-momentum conservation law holds then there should not be any variation in the gravitational coupling with respect to the space time or otherwise the ordinary energymomentum conservation law will be violated [27,28]. In the light of Dirac's idea [29,30,31] which propose that some of the fundamental constants cannot remain constant forever, it is essential to do some modifications in GR field equations [32,33] if we are to consider this running cosmological constant term.…”