Modified Dispersion Relations and Noncommutative Geometry lead to a finite Zero Point Energy

TL;DR

This paper demonstrates that using Modified Dispersion Relations and Noncommutative Geometry can render Zero Point Energy finite without the need for renormalization, contrasting with traditional methods.

Contribution

It shows that NCG and MDR approaches eliminate divergences in Zero Point Energy calculations, avoiding renormalization.

Findings

Zero Point Energy becomes finite with NCG and MDR

No renormalization needed in these approaches

Divergences are handled via zeta function regularization

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 wit 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.