Constructions of $f(R,G,\mathcal{T})$ Gravity from Some Expansions of the Universe

Abstract

Here we propose the extended modified gravity theory named as $f(R,G,\mathcal{T})$ gravity where $R$ is the Ricci scalar, $G$ is the Gauss-Bonnet invariant and $\mathcal{T}$ is the trace of the stress-energy tensor. We derive the gravitational field equations in $f(R,G,\mathcal{T})$ gravity by taking least action principle. Next we construct the $f(R,G,\mathcal{T})$ in terms of $R$, $G$ and $\mathcal{T}$ in de Sitter as well as power law expansion. We also construct $f(R,G,\mathcal{T})$ if the expansion follows the finite time future singulary (big rip singularity). We investigate the energy conditions in this modified theory of gravity and examine the validities of all energy conditions. Finally, we analyze the stability of the constructed modified gravity.

19 pages, 18 figures

References in corpus (18)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Dynamics of dark energy
• f(R,T) gravity
• Extra force in $f(R)$ modified theories of gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Cosmological Evolution of a Quintom Model of Dark Energy
• Reconstructing Dark Energy
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• Energy Conditions in $f(\mathcal{G},T)$ Gravity
• FRW Cosmology in F(R,T) gravity
• From inflation to dark energy in the non-minimal modified gravity
• DBI-essence
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Noether Symmetry Approach in $f(\mathcal{G},T)$ Gravity
• Extended matter bounce scenario in ghost free $f(R,\mathcal{G})$ gravity compatible with GW170817
• Inevitable ghost and the degrees of freedom in f(R,G) gravity
• Generalised DBI-Quintessence
• Linear growth of matter density perturbations in f(R,G) theories

Cited by in corpus (1)

• Cosmological Tests of $f(R,G,T)$ Dark Energy Model in FRW Universe