The 1-loop effective potential for the Standard Model in curved spacetime

TL;DR

This paper calculates the one-loop effective potential of the Standard Model in curved spacetime, revealing how curvature influences vacuum stability and other cosmological phenomena.

Contribution

It provides the first comprehensive computation of the renormalisation group improved effective potential in arbitrary curved spacetime at one loop.

Findings

Potential depends significantly on spacetime curvature.

Curvature effects are crucial for cosmological applications.

Vacuum stability in de Sitter space is affected by curvature.

Abstract

The renormalisation group improved Standard Model effective potential in an arbitrary curved spacetime is computed to one loop order in perturbation theory. The loop corrections are computed in the ultraviolet limit, which makes them independent of the choice of the vacuum state and allows the derivation of the complete set of $\beta$-functions. The potential depends on the spacetime curvature through the direct non-minimal Higgs-curvature coupling, curvature contributions to the loop diagrams, and through the curvature dependence of the renormalisation scale. Together, these lead to significant curvature dependence, which needs to be taken into account in cosmological applications, which is demonstrated with the example of vacuum stability in de Sitter space.