Effective potential in $SO(N)$ symmetric scalar field theories in curved spacetime

TL;DR

This paper derives recurrence relations for quantum corrections in $SO(N)$ symmetric scalar theories in curved spacetime, providing RG equations for the effective potential, with applications to inflationary cosmology.

Contribution

It introduces a new method for calculating all-loop quantum corrections and RG equations for $SO(N)$ symmetric scalar theories in curved spacetime.

Findings

Derived recurrence relations for quantum corrections.

Obtained RG equations for the effective potential in large N limit.

Applied the framework to power-like potentials in inflationary models.

Abstract

We derive recurrence relations for leading logarithmic all-loop quantum corrections in the case of $SO(N)$ symmetric scalar theory with an arbitrary potential in curved spacetime. On this basis, a system of renormalisation group (RG) equations in the general is obtained approach for the effective potential in the large $N$ limit. As a simple illustration, we analyse the case of power-like potentials in the Jordan frame and discuss their application to inflationary cosmology.