An analytic regularisation scheme on curved space–times with applications to cosmological space–times

Abstract

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