Condensed dark matter with a Yukawa interaction

TL;DR

This paper investigates the phases of condensed fermionic dark matter with Yukawa interactions, analyzing phase transitions, superfluid properties, and astrophysical implications across different parameter regimes.

Contribution

It introduces a comprehensive analysis of phase diagrams and gap equations for Yukawa-coupled fermionic dark matter, including relativistic effects and numerical solutions.

Findings

Delimits BCS, BEC, and crossover phases based on parameters.

Derives and solves gap equations in relativistic and non-relativistic regimes.

Discusses the equation of state and astrophysical implications for dark matter.

Abstract

We explore the possible phases of a condensed dark matter (DM) candidate taken to be in the form of a fermion with a Yukawa coupling to a scalar particle, at zero temperature but at finite density. This theory essentially depends on only four parameters, the Yukawa coupling, the fermion mass, the scalar mediator mass, and the DM density. At low fermion densities we delimit the Bardeen-Cooper-Schrieffer (BCS), Bose-Einstein Condensate (BEC) and crossover phases as a function of model parameters using the notion of scattering length. We further study the BCS phase by consistently including emergent effects such as the scalar density condensate and superfluid gaps. Within the mean field approximation, we derive the consistent set of gap equations, retaining their momentum dependence, and valid in both the non-relativistic and relativistic regimes. We present numerical solutions to the set of gap equations, in particular when the mediator mass is smaller and larger than the DM mass. Finally, we discuss the equation of state (EoS) and possible astrophysical implications for asymmetric DM.