Mass-varying Dark Matter from a Phase Transition

We propose a mass-varying dark matter (MVDM) model consisting of a scalar field and a fermionic field interacting via a simple Yukawa coupling, and containing an exponential self-interaction potential for the scalar field. Analyzing the evolution of this coupled scalar-fermion system in an expanding Universe, we find that it initially behaves like radiation but then undergoes a phase transition after which it behaves like pressureless dark matter. The one free parameter of this model is the temperature at which the phase transition occurs; the mass of the dark matter particle, given by the mass of the fermion, is derived from this. For a phase transition temperature between 10 MeV and $10^7$ GeV, the current dark matter relic density is achieved for a fermion mass in the range of 1 GeV to $10^9$ GeV. In this dark matter model, the scalar becomes a sub-dominant unclustered component of dark matter that can lower the amplitude of structure formation by up to a few percent. Another feature is that the mass-varying fermion component can lead to discrepant measurements of the current dark matter density of about ten percent inferred from early and late-time probes assuming LCDM.