Ultraviolet Regularisation in de Sitter Space

TL;DR

This paper investigates ultraviolet regularisation of Yukawa theory in de Sitter space, deriving effective potentials consistent with flat space results, and discusses implications for inflationary cosmology and quantum field theory.

Contribution

It rederives one-loop effective potentials in de Sitter space using dimensional regularisation, ensuring invariance and absence of anomalous de Sitter breaking, with implications for inflation.

Findings

Effective potentials match flat space Coleman-Weinberg results.

Self-energies are invariant under regularisation.

No anomalous de Sitter breaking terms are found.

Abstract

The ultraviolet regularisation of Yukawa theory in de Sitter space is considered. We rederive the one-loop effective Candelas-Raine potentials, such that they agree with the corresponding Coleman-Weinberg potentials in flat space. Within supersymmetry, this provides a mechanism for the lifting of flat directions during inflation. For the purpose of calculating loop integrals, we employ the dimensional regularisation procedure by Onemli and Woodard and show explicitly that the resulting self-energies are also invariant. This implies the absence anomalous de Sitter breaking terms, which are reported in the literature. Furthermore, transplanckian effects do not necessarily leave an imprint on the spectrum of cosmic perturbations generated during inflation.