The Cosmological constant and the Wheeler-DeWitt Equation

TL;DR

This paper explores how the cosmological constant can be derived from the Wheeler-DeWitt equation by approximating it as an eigenvalue problem, using variational methods, mode decomposition, and regularization techniques.

Contribution

It introduces a novel approach to extract the cosmological constant from the Wheeler-DeWitt equation employing a one-loop approximation and a variational method with Gaussian wave functionals.

Findings

No ghosts appear in the evaluation of the cosmological constant.

A zeta function regularization effectively handles divergences.

Renormalization and renormalization group equations are used to address infinities.

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. 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 is used to handle with divergences. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation. A brief discussion on the extension to a $f(R)$ theory is considered.