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Regular Article - Theoretical Physics

Stellar structure of quark stars in a modified Starobinsky gravity Arun Mathewa , Muhammed Shafeequeb , Malay K. Nandyc Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, India

Received: 3 November 2019 / Accepted: 9 June 2020 © The Author(s) 2020

Abstract We propose a form of gravity–matter interaction given by ω RT in the framework of f (R, T ) gravity and examine the effect of such interaction in spherically symmetric compact stars. Treating the gravity–matter coupling as a perturbative term on the background of Starobinsky gravity, we develop a perturbation theory for equilibrium configurations. For illustration, we take the case of quark stars and explore their various stellar properties. We find that the gravity–matter coupling causes an increase in the stable maximal mass which is relevant for recent observations on binary pulsars.

1 Introduction Modern day scenarios such as inflation [1,2], late-time cosmic acceleration [3–5], flat rotation curves [6–9] etc. are incompatible with the standard prescription of general relativity (GR). Although the predictions of GR in the weakfield regime are precise, it falls short in the higher curvature regime in the sense that it predicts singularities such as the big bang and the black hole singularities. It has been shown that quantum corrections generate higher order self-coupling curvature in addition to the original scalar curvature [10,11]. This motivates one to consider non-linear curvature theories to see if they provide a better descriptions of gravitation phenomena. A nonlinear curvature theory of gravity was proposed by Starobinsky [12] in order to address the issue of the bigbang singularity. He considered the Einstein field equations G μν = κTμν  where the right hand side gives quantum mechanical contributions due to coupling between quantum matter fields (having different spins) with classical gravitational field, with the assumption of isotropy and homogeneity a e-mail:

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and absence of radiation field. In one-loop approximation, and upon regularization, Tμν  was found to be a function of the Riemann geometric quantities. Based on these findings, Starobinsky exhibited the existence of a one-parameter family of non-singular solutions of the de-Sitter type which could be analytically continued into the region t < 0. The deSitter phase naturally explains the inflation scenario without having to include any inflaton field. However, another approach involves a generalization of the Einstein–Hilbert action where an arbitrary function f (R) represents the Lagrangian density [13]. In the Starobinsky model, namely, f (R) = R + α R 2 , and its other generalisations, inflation has been explained to obtain increasingly better fits the observational data [14,15]. Moreover, various forms of f (R) gravity have been able to explain the late-time cosmic acceleration [15