On the renormalization procedure for quantum fields with modified dispersion relation in curved spacetimes

TL;DR

This paper reviews the renormalization process for quantum scalar fields with modified dispersion relations in curved spacetimes, highlighting how the subtraction depends on the dispersion relation's order and extending analysis to general metrics.

Contribution

It provides a new power counting analysis for renormalization in general background metrics, expanding previous flat spacetime results.

Findings

Renormalization subtraction depends on the order of dispersion relation s.

Analysis extended from flat to general background metrics.

New power counting method developed for weak field approximation.

Abstract

We review our recent results on the renormalization procedure for a free quantum scalar field with modified dispersion relations in curved spacetimes. For dispersion relations containing up to $2s$ powers of the spatial momentum, the subtraction necessary to renormalize $<\phi^2>$ and $<T_{\mu\nu}>$ depends on $s$. We first describe our previous analysis for spatially flat Friedman-Robertson-Walker and Bianchi type I metrics. Then we present a new power counting analysis for general background metrics in the weak field approximation.