Tidal deformability of dark energy stars in gravity's rainbow

Abstract

We present a self-consistent model of isotropic dark energy stars constructed within the framework of Gravity's Rainbow (GRw), a quantum-gravity-motivated extension of general relativity that incorporates Planck-scale corrections via energy-dependent rainbow functions. The interior matter content is modeled using a modified Chaplygin gas equation of state, which smoothly interpolates between barotropic fluid behavior and vacuum energy. The gravitational equilibrium of the star is governed by a rainbow-deformed Tolman-Oppenheimer-Volkoff (TOV) system, which accounts for ultraviolet modifications to the geometry through the rainbow functions equivalent to(x) and Sigma(x). By numerically solving these equations across a broad range of central densities and rainbow function scalings, we analyze global observables such as the gravitational mass, radius, and compactness. We find that sub-unitary spatial rainbow functions significantly raise the maximum gravitational mass into the range between heavy neutron stars and low-mass black holes, without invoking an event horizon. Our results identify a wide and viable parameter space for constructing horizonless compact objects compatible with current astrophysical constraints, highlighting the physical richness introduced by the influence of Planck-scale spacetime deformations on isotropic dark energy stars.