Constructions of f(R,G,𝒯) gravity from some expansions of the Universe

Abstract

Here we propose the extended modified gravity theory named [Formula: see text] gravity where [Formula: see text] is the Ricci scalar, [Formula: see text] is the Gauss–Bonnet invariant, and [Formula: see text] is the trace of the stress-energy tensor. We derive the gravitational field equations in [Formula: see text] gravity by taking the least action principle. Next we construct the [Formula: see text] in terms of [Formula: see text], [Formula: see text] and [Formula: see text] in de Sitter as well as power-law expansion. We also construct [Formula: see text] if the expansion follows the finite-time future singularity (big rip singularity). We investigate the energy conditions in this modified theory of gravity and examine the validity of all energy conditions.