Quantum cosmology near two dimensions

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 the Ward identities in a nontrivial way. The resulting evolution equations for an isotropic, homogeneous universe lead to slowly decaying vacuum energy and power-law expansion. We outline the implications for the cosmological constant problem, inflation, and dark energy.