Abstract This paper explores the internal composition and equation of state (EoS) of quark stars (QSs) characterised by pressure anisotropy, considering recent astrophysical findings within the framework of gravity's rainbow. By employing perturbative quantum chromodynamics (QCD) corrections and the concept of color superconductivity, the EoS was formulated as a dimensionless function reliant on a single parameter, thereby offering an in-depth analysis of the effects of strong interactions. The study is further extended by rescaling the EoS and applying dimensionless variables, thus covering a range from non-interacting quark matter to extreme stiffness characterized by a parameter. We also show that including the fluid anisotropy permits stiffer EoS, facilitating the modelling of configurations that adequately meet observational constraints. We then use the supposed EoSs to numerically solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations and examine the effects of anisotropy and rainbow parameters on star mass, radius, and compactness. The paper also explores the static stability, the adiabatic index, and sound velocity profiles, thoroughly explaining QS behaviour. Overall, this study offers valuable insights into the characteristics of QSs and their consistency with observational data, providing a comprehensive analysis of their EoS and internal structure.
Banerjee et al. (Tue,) studied this question.