An analytic regularisation scheme on curved spacetimes with applications to cosmological spacetimes

TL;DR

This paper introduces an analytic regularisation and minimal subtraction scheme for renormalising time-ordered products in interacting quantum field theories on curved spacetimes, applicable to cosmological models and preserving covariance.

Contribution

It presents a novel, covariant renormalisation scheme based on analytic regularisation, suitable for practical computations in curved spacetimes, including cosmological applications.

Findings

Scheme is manifestly covariant and invariant under spacetime isometries.

Explicit computations demonstrate applicability to cosmological spacetimes.

The method captures non-geometric, state-dependent contributions of Feynman amplitudes.

Abstract

We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to spacetimes with Lorentzian signature, manifestly generally covariant, invariant under any spacetime isometries present and constructed to all orders in perturbation theory. Moreover, the scheme captures correctly the non--geometric state--dependent contribution of Feynman amplitudes and it is well--suited for practical computations. To illustrate this last point, we compute explicit examples on a generic curved spacetime, and demonstrate how momentum space computations in cosmological spacetimes can be performed in our scheme. In this work, we discuss only scalar fields in four spacetime dimensions, but we argue that the renormalisation scheme can be directly generalised to other spacetime dimensions and field theories with higher spin, as well as to theories with local gauge invariance.