Sterile Neutrinos as a Dynamical Cosmological Fluid: Implications for the Expansion History and Matter-Radiation Equality

TL;DR

This paper develops an analytic model treating sterile neutrinos as a dynamic fluid with a time-varying equation of state, impacting cosmological expansion and matter-radiation equality.

Contribution

It introduces a framework linking sterile neutrino production physics to cosmological evolution, surpassing the standard Delta Neff approximation.

Findings

Sterile neutrinos with incomplete thermalization have a time-dependent equation of state.

Their energy density can become matter-like at matter-radiation equality.

The contribution of sterile neutrinos remains small according to observational constraints.

Abstract

Sterile neutrinos arise naturally in extensions of the Standard Model and can affect cosmological evolution even with subdominant abundance. Their impact is often described by a constant shift in the effective number of relativistic species, Delta Neff, assuming a radiation-like equation of state. However, for finite mass sterile neutrinos with incomplete thermalization, the equation of state evolves with time. In this work, we develop an analytic framework treating sterile neutrinos as a dynamical cosmological fluid with a time-dependent equation of state. Starting from the Boltzmann equation in an expanding Friedmann-Lemaitre-Robertson-Walker background, we show that suppressed active-sterile oscillations lead to a reduced Fermi-Dirac distribution characterized by a thermalization parameter less than unity. We compute the resulting energy density and pressure and incorporate them into the Friedmann equations. We identify distinct regimes, including a relativistic phase, a transition phase, and a matter-like behavior. For GeV scale sterile neutrinos, their contribution at matter-radiation equality is effectively matter-like, shifting the equality epoch in proportion to their energy fraction. Observational constraints indicate that this fraction remains small. This framework connects microscopic production physics to cosmological expansion and goes beyond the standard Delta Neff description.