Modified Gravity Description of Neutron Star in the f(R) Framework

Abstract

The present paper reports a study on neutron stars in the f(R) gravity framework for the Hu–Sawicki model, Starobinsky model, Tsujikawa model, and Exponential Gravity model. First, we have used the TOV equation for the f(R) gravity framework, where we obtained two higher order differential equations for λ and ψ, with both functions depending on the radial coordinate. Furthermore, we have considered the BD theory, which is an equivalent theory of f(R) gravity, and introduced a new scalar field ϕ2 with the scalar potential V(ϕ2). We have observed an increase in the scalar potential with respect to R in each case. Furthermore, our proposed models, namely quadratic form, exponential form, and linear form and the other viable models show a similar type of evolution for the scalar potential V(ϕ2).