Cosmology of strongly interacting fermions in the early universe
  In view of growing interest in long range scalar forces in the early universe
to generate primordial black holes, we study in detail the general relativistic
formulation of a Fermi gas interacting with a scalar field in cosmology. Our
main finding is that the Yukawa interaction leads to a solution where the
scalar field oscillates around zero fermion mass and all energy densities decay
as radiation. On one hand, we show that if the Fermi gas starts relativistic,
it could stay relativistic. On the other hand, if the fermions are initially
non-relativistic, they remain non-relativistic for all practical purposes. We
find that in both cases the energy density of the fermions and the scalar field
decays as radiation. In the non-relativistic case, this is due to an
oscillating and decaying effective mass. Such background dynamics questions
whether there is a substantial enhancement of the fermion density fluctuations
in the non-relativistic case. Our work can be easily extended to more general
field dependent fermion mass. The analysis of the cosmological perturbations
will be presented in a follow-up work.
