Extracting the Cosmological Constant from the Wheeler DeWitt Equation in a Modified Gravity Theory

TL;DR

This paper investigates how to determine the cosmological constant from the Wheeler-DeWitt equation within a modified gravity framework, employing variational methods and zeta function regularization to handle divergences.

Contribution

It extends the Wheeler-DeWitt equation analysis to f(R) gravity theories and introduces a variational approach with Gaussian wave functionals for one-loop approximation.

Findings

Derived a method to extract the cosmological constant as an eigenvalue.

Applied zeta function regularization to manage divergences.

Developed a renormalization procedure and renormalization group equation.

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. A generalization to a f(R)theory is taken under examination. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. We use a zeta function regularization to handle with divergences. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.