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

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