Gravitational Zero Point Energy and the Induced Cosmological Constant

TL;DR

This paper explores how the Wheeler-DeWitt equation can be used to estimate the cosmological constant by applying a one-loop approximation, variational methods, and regularization techniques in a spherically symmetric background.

Contribution

It introduces a novel approach to derive the cosmological constant from quantum gravity considerations using a variational and regularization framework.

Findings

No ghosts appear in the final cosmological constant evaluation

Regularization and renormalization effectively handle divergences

Comparison with noncommutative geometry results provides insights

Abstract

We discuss how to extract information about the cosmological constant from the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem in a generic spherically symmetric background. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. A canonical decomposition of modes is used to separate transverse-traceless tensors (graviton) from ghosts and scalar. We show that no ghosts appear in the final evaluation of the cosmological constant. A zeta function regularization and a ultra violet cutoff are used to handle with divergences. A renormalization procedure is introduced to remove the infinities. We compare the result with the one obtained in the context of noncommutative geometries