Comparison of energy conditions in general relativity and modified theories of gravity

Abstract

To make a comparison of energy conditions in the theory of general relativity and in the modified theories, we have considered [Formula: see text], [Formula: see text] and [Formula: see text] theories (where [Formula: see text] and [Formula: see text] are the Ricci scalar and trace of the energy–momentum tensor, respectively, while [Formula: see text]) to test the validity of all the four energy conditions. These energy conditions had been derived to check the viability of cosmological as well as astrophysical models. In this paper, we consider the standard Friedmann–Robertson–Walker spacetime representing the homogeneous and isotropic universe, and investigate the available literature on testing energy conditions as well as calculate these conditions ourselves. In order to provide the comparative results, we test these conditions analytically as well as graphically and present how energy bounds in modified theories depend on the values of the involved parameters and its validity within certain limits. We discuss here, that which of the modified theories comply with certain energy conditions, and hence provide a supporting argument on the existence of modified theories.