  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.
