Dark energy stars and quark stars within the context of [formula omitted] gravity

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In this work, we investigate the relativistic structure of compact stars within the framework of f(Q) gravity, where Q is the nonmetricity scalar. In particular, we focus on the f(Q)=αQ+β gravity model, with α and β being free parameters of the theory. This study is split up into: 1. Models of dark energy stars by using metric potentials of Tolman–Kuchowicz type which are free of singularity. It considers the stellar fluid to be made up of both ordinary matter along with dark energy, where the constants in the metric are determined from observational measurements of some well-known compact stars. Part 2 deals with quark stars where their masses and radii are a consequence of integrating the stellar structure equations given a specific equation of state (EoS) for the dense matter involved. We use the pulsar SAX J1808.4-3658, which has a known mass and radius of M=0.9−0.3+0.3M⊙, and 7.95−1+1km respectively, to explain the physical characteristics of the dark energy star. For various values of α, the causality criteria and the model’s dynamical stability are discussed. In light of the discovery of gravitational waves GW190814, we also investigate the possibility of characterizing the secondary component of such an event as a stable dark energy star in the presence of anisotropy using the M−R relation, which characterizes a dark energy star with mass 2.57M⊙ and associated radius 9.3km. Furthermore, in the case of quark stars with MIT bag model EoS, we find that both the radius and the mass increase with increasing α for fixed β=0. Meanwhile, the effect of the parameter β is a substantial increase in the maximum-mass values as β becomes more negative for a fixed value of α.