Impact of projective curvature tensor in $f\left(R,G\right)$, $f\left(R,T\right)$ and $f\left(R,L_m\right)$-gravity

Abstract

This article concerns with the characterization of a spacetime and modified gravity, such as $f\left(R,G\right)$, $f\left(R,T\right)$ and $f\left(R,L_m\right)$-gravity equipped with the projective curvature tensor. We establish that a projectively flat perfect fluid spacetime represents dark energy era. Also, we prove that a projectively flat perfect fluid spacetime is either locally isometric to Minkowski spacetime or a de-Sitter spacetime. Furthermore, it is shown that a perfect fluid spacetime permitting harmonic projective curvature tensor becomes a generalized Robertson-Walker spacetime and is of Petrov type $I$, $D$ or $O$. Lastly, we investigate the effect of projectively flat perfect fluid spacetime solutions in $f\left(R,G\right)$, $f\left(R,T\right)$ and $f\left(R,L_m\right)$-gravity, respectively. We also investigate the spacetime as a $f\left(R,G\right)$-gravity solution of and use the flat Friedmann-Robertson-Walker metric to establish a relation among jerk, snap, and deceleration parameters. Numerous energy conditions are studied in terms of Ricci scalar with the model $f\left(R,G\right)=\exp (R)+\alpha {\left(6G\right)}^{\beta }$. For this model, the strong energy condition is violated but the weak, dominant and null energy conditions are fulfilled, which is in excellent accordance with current observational investigations that show the universe is now accelerating.

References in corpus (28)

• f(R,T) gravity
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Extra force in $f(R)$ modified theories of gravity
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• f(R,L_m) gravity
• Modified gravity with arbitrary coupling between matter and geometry
• Cosmological inflation in $F(R,\mathcal{G})$ gravity
• LambdaCDM epoch reconstruction from F(R,G) and modified Gauss-Bonnet gravities
• A simple characterization of generalized Robertson-Walker spacetimes
• Cosmology with a stiff matter era
• Generalized Robertson-Walker space times, a survey
• The role of energy conditions in $f(R)$ cosmology
• An Alternative f (R, T) Gravity Theory and the Dark Energy Problem
• Energy conditions in $f(R,G)$ gravity
• Energy Conditions in Modified $f(G)$ Gravity
• On the stability of the cosmological solutions in f(R,G) gravity
• Constraining f(R) theories with the energy conditions
• A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time
• Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension
• Newtonian, Post Newtonian and Parameterized Post Newtonian limits of f(R, G) gravity
• Yang's gravitational theory
• Limits on $f(R,T)$ Gravity from Earth's Atmosphere
• Cosmological perfect fluids in Gauss-Bonnet gravity
• How a projectively flat geometry regulates $F(R)$-gravity theory?
• FLRW-Cosmology in Generic Gravity Theories
• Characterizations of a spacetime of quasi-constant sectional curvature and $\mathcal{F}(\mathcal{R})$-gravity
• Geometric Perfect Fluids from Extended Gravity