# Bounds on Higher Derivative $f(R,\square R,T)$ Models from Energy Conditions

## TL;DR

This paper explores the constraints on higher derivative $f(R,ox R,T)$ gravity models using energy conditions within a flat FLRW universe, identifying viable cosmological solutions through numerical analysis of cosmic parameters.

## Contribution

It introduces a method to determine viable regions of $f(R,ox R,T)$ models using energy conditions and numerical cosmic parameters in a flat FLRW setting.

## Key findings

- Identified viable zones for specific $f(R,ox R,T)$ models.
- Demonstrated the use of energy conditions to constrain higher derivative gravity models.
- Provided numerical analysis of cosmic parameters to support stability of solutions.

## Abstract

This paper studies the viable regions of some cosmic models in a higher derivative $f(R,\square R, T)$ theory with the help of energy conditions (where $R$ and $T$ are the Ricci scalar, and trace of energy momentum tensor, respectively). For this purpose, we assume a flat Friedmann-Lema\^{i}tre-Robertson-Walker metric which is assumed to be filled with perfect fluid configurations. We take two distinct realistic models, that might be helpful to explore stable regimes of cosmological solutions. After taking some numerical values of cosmic parameters, like crackle, snap, jerk (etc) as well as viable constraints from energy conditions, the viable zones for the under observed $f(R,\square R, T)$ models are examined.