Gravitational Imprints of Dark Energy in Neutron Stars

Abstract

We investigate, for the first time, the non-radial $f$-mode oscillations of neutron stars (NSs) with a dark energy (DE) core utilising a fully general relativistic treatment. We construct the stellar profile by considering a relativistic mean field model for nuclear matter and a modified Chaplygin fluid like prescription for DE. We compute the stellar structure, $f$-mode oscillations, tidal deformability, and gravitational wave (GW) energy and strain of the NS with DE core by varying the DE equation of state (EoS) parameters. Our study reveals that the inclusion of DE softens EoS and reduces the maximum mass compared to the pure neutron star. The obtained mass-radius values are consistent with observational constraints from massive pulsars such as PSR J0030+0451 and PSR J0740+6620. We find that the extent of the DE core, determined by the transition density, plays a crucial role in modifying the stellar structure and oscillation properties, with lower transition densities producing appreciable changes over a wider mass range. The $f$-mode frequencies and damping times exhibit systematic modifications, for higher mass configurations, while the correlation between the $f$-mode frequency and tidal deformability remains consistent with observational constraints from GW170817 and GW190814. Further, the normalised oscillation energy distribution remains nearly universal, with only minimal deviations for the higher mass configurations. Finally, we estimate the characteristic GW strain associated with the $f$-mode oscillations and find that the predicted signals lie within the sensitivity band of future third generation GW detectors.