Constraints on Energy Conditions in $f(R,L_m)$ Gravity

TL;DR

This paper explores energy conditions in $f(R,L_m)$ gravity, deriving equations and constraints that support the universe's current accelerated expansion, extending the understanding of modified gravity theories.

Contribution

It derives energy conditions and cosmographic constraints in $f(R,L_m)$ gravity, providing new insights into the theory's viability for explaining cosmic acceleration.

Findings

Model supports current accelerated expansion

Constraints on model parameters derived from cosmography

Energy conditions analyzed in the $f(R,L_m)$ framework

Abstract

In this manuscript, we consider the extension of the Hilbert-Einstein action to analyze several interesting features of the theory. More specifically, the Lagrangian $f(R)$ is replaced by $f(R, L_m)$ in action, where $R$ is the Ricci scalar, and $L_m$ is the matter Lagrangian. We derive the motion equations for a test particle in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) flat and homogeneous spacetime. We also derive the energy conditions in this framework. Then, we use the cosmographic parameter such as Hubble, deceleration, jerk, and snap parameters to constraint the model parameters. As a result, we observe that with the constraint range of model parameters our model shows the current accelerated expansion of the universe.