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

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.

3 pages; contribution to the proceedings of the Thirteenth Marcel Grossmann Meeting, Stockholm University, Sweden, 1-7 July, 2012; based on a talk in the ST1"Planckian and Transplanckian Physics" parallel session