Effects of Modified Dispersion Relations and Noncommutative Geometry on the Cosmological Constant Computation

TL;DR

This paper investigates how Modified Dispersion Relations and Noncommutative Geometry influence the calculation of the cosmological constant through quantum gravitational effects, revealing divergence-free results without renormalization.

Contribution

It introduces a novel approach to compute the cosmological constant using Wheeler-DeWitt equation with NCG and MDR, avoiding traditional renormalization.

Findings

No renormalization needed in NCG and MDR approaches

Divergences handled via zeta function regularization

Photon propagation effects briefly discussed

Abstract

We compute Zero Point Energy in a spherically symmetric background with the help of the Wheeler-DeWitt equation. This last one is regarded as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The graviton contribution, at one loop is extracted with the help of a variational approach together with Gaussian trial functionals. The divergences handled with a zeta function regularization are compared with the results obtained using a Noncommutative Geometry (NCG) and Modified Dispersion Relations (MDR). In both NCG and MDR no renormalization scheme is necessary to remove infinities in contrast to what happens in conventional approaches. Effects on photon propagation are briefly discussed.