Anisotropic Dark Matter Stars with a Pressure-Sourced Dark Energy Density

Abstract

If the dark sector is not inert, the vacuum energy trapped inside a dark matter star need not equal its cosmological value, but may instead respond to the star's own density and pressure. We show that this freedom is far more restricted than it first appears: demanding a smooth, physically sensible stellar surface rules out the response one would most naturally try, in which the vacuum energy simply tracks the local density, since it drives the sound speed superluminal in the outer layers. The simplest response that survives is one sourced by the local pressure rather than the density, and we adopt it within an established anisotropic dark matter star model, obtaining the full stellar structure in closed form. The resulting star is heavier than its uncoupled counterpart, by almost $30\%$ at the causal limit, yet correspondingly less strongly supported by pressure, so that the coupling is bounded not by any failure of pressure support but by the star's compactness approaching the threshold for gravitational collapse. We show, further, that once this response is switched on, causality is always the tightest physical requirement upon the star, rendering the dominant energy condition redundant throughout the admissible parameter space.