On the functional renormalization group for the scalar field on curved background with non-minimal interaction

TL;DR

This paper investigates how the non-minimal coupling parameter of a scalar field evolves under the functional renormalization group in curved spacetime, providing insights into its non-perturbative behavior.

Contribution

It derives the RG flow equation for the non-minimal coupling in curved space and explores its numerical trajectories for various initial conditions.

Findings

The RG flow of the non-minimal parameter is characterized in curved spacetime.

Numerical analysis reveals the behavior of the non-minimal coupling under different initial conditions.

Abstract

The running of the non-minimal parameter (\xi) of the interaction of the real scalar field and scalar curvature is explored within the non-perturbative setting of the functional renormalization group (RG). We establish the RG flow in curved space-time in the scalar field sector, in particular derive an equation for the non-minimal parameter. The RG trajectory is numerically explored for different sets of initial data.