Modified Dispersion Relations lead to a finite Zero Point Gravitational Energy

TL;DR

This paper calculates the Zero Point Energy in a high-energy distorted background using Gravity's Rainbow, showing that modified dispersion relations can regularize divergences and relate to the cosmological constant.

Contribution

It introduces a novel approach to handle divergences in Zero Point Energy calculations via modified dispersion relations in Gravity's Rainbow, connecting quantum fluctuations to cosmological observations.

Findings

Divergences are regularized by choosing appropriate rainbow functions.

The approach links quantum fluctuations to the observed cosmological constant.

The method reformulates the Wheeler-DeWitt equation in a Sturm-Liouville framework.

Abstract

We compute the Zero Point Energy in a spherically symmetric background distorted at high energy as predicted by \textit{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. With the help of a canonical decomposition, we find that the relevant contribution to one loop is given by the graviton quantum fluctuations around the given background. By means of a variational approach based on gaussian trial functionals, 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. A final discussion on the connection of our result with the observed cosmological constant is also reported.