Cosmology of strongly interacting fermions in the early universe

TL;DR

This paper investigates the behavior of a fermion gas interacting with a scalar field in the early universe, revealing that the energy densities decay as radiation regardless of initial relativistic conditions, with implications for primordial black hole formation.

Contribution

It provides a detailed general relativistic analysis of fermion-scalar interactions in cosmology, showing that energy densities decay as radiation and exploring conditions for relativistic behavior.

Findings

Scalar field oscillates around zero fermion mass.

Energy densities decay as radiation in both relativistic and non-relativistic cases.

Non-relativistic fermions remain non-relativistic due to oscillating effective mass.

Abstract

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.