The Large Distance Limit of the Gravitational Effective Action in Hyperbolic Backgrounds

TL;DR

This paper analyzes the one-loop effective action in D-dimensional quantum gravity with negative cosmological constant on hyperbolic backgrounds, deriving an explicit curvature expansion and discussing cosmological constant suppression.

Contribution

It provides an explicit power series expansion of the effective action using heat-kernel and zeta-regularization techniques for hyperbolic spaces, advancing understanding of quantum gravity effects.

Findings

Derived explicit curvature expansion of the effective action

Demonstrated Coleman-Weinberg suppression of the cosmological constant

Applied heat-kernel and zeta-regularization methods to hyperbolic backgrounds

Abstract

The one-loop effective action for D-dimensional quantum gravity with negative cosmological constant, is investigated in space-times with compact hyperbolic spatial section. The explicit expansion of the effective action as a power series of the curvature on hyperbolic background is derived, making use of heat-kernel and zeta-regularization techniques. It is discussed, at one-loop level, the Coleman-Weinberg type suppression of the cosmological constant, proposed by Taylor and Veneziano.