Ultraviolet cutoffs for quantum fields in cosmological spacetimes

TL;DR

This paper investigates the effects of non covariant ultraviolet cutoffs on the renormalization process of quantum fields in cosmological spacetimes, highlighting differences from covariant approaches and implications for semiclassical Einstein equations.

Contribution

It provides explicit calculations of counterterms for renormalization using comoving and physical UV cutoffs, revealing how non covariant methods alter the resulting equations.

Findings

Renormalized equations differ from covariant methods.

Divergences renormalize conserved fluids in comoving cutoff case.

Breaking covariance is necessary with physical cutoffs.

Abstract

We analyze critically the renormalization of quantum fields in cosmological spacetimes, using non covariant ultraviolet cutoffs. We compute explicitly the counterterms necessary to renormalize the semiclassical Einstein equations, using comoving and physical ultraviolet cutoffs. In the first case, the divergences renormalize bare conserved fluids, while in the second case it is necessary to break the covariance of the bare theory. We point out that, in general, the renormalized equations differ from those obtained with covariant methods, even after absorbing the infinities and choosing the renormalized parameters to force the consistency of the renormalized theory. We repeat the analysis for the evolution equation for the mean value of an interacting scalar field