Energy conditions in $f(R,L_{m})$ gravity

TL;DR

This paper derives general energy conditions for the $f(R,L_{m})$ gravity theory, which can be specialized to known theories, and applies them to a cosmological model using observational data to constrain the theory.

Contribution

It provides the first derivation of general energy conditions in $f(R,L_{m})$ gravity, unifying and extending previous conditions in related theories.

Findings

Derived general energy conditions for $f(R,L_{m})$ gravity.

Showed how these conditions reduce to known cases in specific limits.

Applied the conditions to a cosmological model with observational constraints.

Abstract

In order to constrain $f(R,L_{m})$ gravity from theoretical aspects, its energy conditions are derived in this paper. These energy conditions given by us are quite general and can be degenerated to the well-known energy conditions in General Relativity and $f(R)$ theories of gravity with arbitrary coupling, non-minimal coupling and non-coupling between matter and geometry, respectively, as special cases. To exemplify how to use these energy conditions to restrict $f(R,L_{m})$ gravity, we consider a special model in the FRW cosmology and give some corresponding results by using astronomical observations.