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 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.

34 pages, 1 figure

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• An Improved Cosmological Model
• Nonlocal Quantum Effective Actions in Weyl-Flat Spacetimes
• Quantum Cosmology in Four Dimensions
• Gravitational action for a massive Majorana fermion in 2d quantum gravity