Impact of curvature based geometric constraints on $F(R)$ theory

Abstract

Theories of gravity are fundamentally a relation between matter and the geometric structure of the underlying spacetime. So once we put some additional restrictions on the spacetime geometry, the theory of gravity is bound to get the impact, irrespective of whether it is general relativity or the modified theories of gravity. In the present article, we consider two curvature-based constraints, namely the almost pseudo-Ricci symmetric and weakly Ricci symmetric condition. As a novel result, such spacetimes with non-null associated vectors are entirely classified, and then applying the obtained results, we investigate these spacetimes as solutions of the $F(R)$-gravity theory. The modified Friedmann equations are derived and analysed in a model-independent way first. Finally, two $F(R)$ gravity models are examined for recent observational constrained values of the deceleration, jerk, and Hubble parameters. We further discuss the behavior of energy conditions.

EPJC accepted version

References in corpus (22)

• Disappearing cosmological constant in f(R) gravity
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Conditions for the cosmological viability of f(R) dark energy models
• Extended Gravity Cosmography
• Energy conditions in f(R)-gravity
• The Raychaudhuri equations: a brief review
• Energy Conditions in Modified $f(G)$ Gravity
• Constraining f(R) theories with the energy conditions
• Unification of Inflation with Dark Energy in $f(R)$ Gravity and Axion Dark Matter
• Energy conditions in f(R) gravity and Brans-Dicke theories
• Energy conditions and current acceleration of the universe
• Perfect-fluid, generalised Robertson-Walker space-times, and Gray's decomposition
• 6+1 lessons from f(R) gravity
• A Conformally Flat Generalized Ricci Recurrent Spacetime in F(R)-Gravity
• "Detuned" f(R) gravity and dark energy
• Energy conditions for a $(WRS{)}_4$ spacetime in $F(R)$-gravity
• How a projectively flat geometry regulates $F(R)$-gravity theory?
• Almost pseudo-Ricci symmetric spacetime solutions in $F(R)$-gravity
• Geometric Perfect Fluids from Extended Gravity
• A complete study of conformally flat pseudo-symmetric spacetimes in the theory of F(R)-gravity
• A classification of conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds

Cited by in corpus (1)

• A constrained cosmological model in $f(R,L_m)$ gravity