Renormalized stress-energy tensor for spin-1/2 fields in expanding universes

TL;DR

This paper derives an explicit, UV-finite expression for the renormalized stress-energy tensor of spin-1/2 fields in expanding universes using an extended adiabatic regularization method, with applications to cosmological models.

Contribution

It extends adiabatic regularization to fermion fields and provides a practical method to compute the stress-energy tensor in cosmological spacetimes.

Findings

Explicit formulas for the renormalized stress-energy tensor in FLRW universes.

Demonstration of the method in de Sitter and radiation-dominated universes.

Late-time behavior of the tensor matches classical cold matter in radiation universe.

Abstract

We provide an explicit expression for the renormalized expectation value of the stress-energy tensor of a spin-$1/2$ field in a spatially flat FLRW universe. Its computation is based on the extension of the adiabatic regularization method to fermion fields introduced recently in the literature. The tensor is given in terms of UV-finite integrals in momentum space, which involve the mode functions that define the quantum state. As illustrative examples of the method efficiency, we see how to compute the renormalized energy density and pressure in two interesting cosmological scenarios: a de Sitter spacetime and a radiation-dominated universe. In the second case, we explicitly show that the late-time renormalized stress-energy tensor behaves as that of classical cold matter. We also check that, if we obtain the adiabatic expansion of the scalar field mode functions with a similar procedure to the one used for fermions, we recover the well-known WKB-type expansion.