Finite Zero Point Gravitational Energy in the context of Modified Dispersion Relations

TL;DR

This paper calculates the Zero Point Energy in a modified gravity framework called Gravity's Rainbow, showing that divergences can be managed through specific functions, offering a new approach to quantum gravitational energy calculations.

Contribution

It introduces a novel method to handle divergences in Zero Point Energy calculations using Gravity's Rainbow, reformulating the Wheeler-DeWitt equation with a Sturm-Liouville problem.

Findings

Divergences are controllable via rainbow functions.

Reformulation of Wheeler-DeWitt equation as Sturm-Liouville problem.

Zero Point Energy computed in a high-energy distorted background.

Abstract

We compute the Zero Point Energy in a spherically symmetric background distorted at high energy as predicted by Gravity's Rainbow. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation. We find that the ordinary divergences can here be handled by an appropriate choice of the rainbow's functions, in contrast to what happens in other conventional approaches.