Quantum Cosmology Near Two Dimensions

TL;DR

This paper explores a Weyl-invariant gravity model near two dimensions, revealing a connection to Liouville theory and implications for cosmological constant, inflation, and dark energy.

Contribution

It introduces a Weyl-invariant formulation of gravity near two dimensions and analyzes its quantum effects on cosmological evolution.

Findings

Quantum momentum tensor is nonlocal and satisfies Ward identities.

Universe exhibits slowly decaying vacuum energy and power-law expansion.

Implications for cosmological constant problem, inflation, and dark energy.

Abstract

We consider a Weyl-invariant formulation of gravity with a cosmological constant in d-dimensional spacetime and show that near two dimensions the classical action reduces to the timelike Liouville action. We show that the renormalized cosmological term leads to a nonlocal quantum momentum tensor which satisfies theWard identities in a nontrivial way. The resulting evolution equations for an isotropic, homogeneous universe lead to a slowly decaying vacuum energy and a power-law expansion. We outline the implications for the cosmological constant problem, inflation, and dark energy.