# Reconstruction of Scalar Potentials in $f(R,R_{\alpha\beta} R^{\alpha\beta},\phi)$ theory of gravity

## TL;DR

This paper reconstructs scalar field potentials in a modified gravity theory using a scheme that relates the Hubble parameter to the scalar field, analyzing specific cosmological models and matter sources.

## Contribution

It introduces a reconstruction method for scalar potentials in $f(R,R_{\alpha\beta} R^{\alpha\beta},\phi)$ gravity and applies it to various cosmological scenarios.

## Key findings

- Reconstructed scalar potentials are cosmologically viable.
- Different matter sources influence the form of scalar potentials.
- The method is applicable to both de Sitter and power law models.

## Abstract

In this paper, we explore the nature of scalar field potential in $f(R, R_{\alpha\beta} R^{\alpha\beta},\phi)$ gravity using a well-motivated reconstruction scheme for flat FRW geometry. The beauty of this scheme lies in the assumption that the Hubble parameter can be expressed in terms of scalar field and vice versa. Firstly, we develop field equations in this gravity and present some general explicit forms of scalar field potential via this technique. In the first case, we take De Sitter universe model and construct some field potentials by taking different cases for coupling function. In the second case, we derive some field potentials using power law model in the presence of different matter sources like barotropic fluid, cosmological constant and Chaplygin gas for some coupling functions. From graphical analysis, it is concluded that using some specific values of the involved parameters, the reconstructed scalar field potentials are cosmologically viable in both cases.