Cosmology in theories with derivative matter coupling

TL;DR

This paper explores a new class of modified gravity theories with derivative matter coupling, analyzing their cosmological implications, energy conservation properties, and compatibility with observational data.

Contribution

It introduces a novel class of $f(L_m)$ gravity theories with derivative matter coupling and examines their cosmological behavior and observational viability.

Findings

Conservative and non-conservative cases identified in FRW background.

Models can satisfy current observational data.

Non-conservative case predicts less matter at early times and more deceleration.

Abstract

A new class of modified gravity theories with a healthy higher order derivative terms of a function of the matter Lagrangian $f(L_m)$ is considered. Generally the energy momentum tensor is not conserved, leading to the fifth force similar to $f(R,T)$ theories. We will however show that in the FRW background there exists two possibilities corresponding to conservative and non-conservative cases. Cosmological implications of both cases with different functions of the matter Lagrangian $f$ will be investigated in details and we will show that current observational data can be satisfied in this model. The non-conservative case however, predicts less matter sources at early times and more deceleration. Evolution of the matter density perturbation in the longitudinal gauge is also considered for dust matter sources. We will show that the late time behavior of the matter density perturbation is in agreement with current observational data at sub-horizon limit.