Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant

TL;DR

This paper explores using Modified Dispersion Relations to regularize divergences in quantum field theory, specifically in black hole entropy calculations and graviton zero-point energy, linking it to the cosmological constant.

Contribution

It introduces a novel regularization scheme based on MDR to address infinities in quantum gravity calculations, offering an alternative to traditional methods.

Findings

MDR regularization successfully computes black hole entropy.

MDR approach provides finite graviton zero-point energy.

Results connect quantum field divergences to the cosmological constant.

Abstract

Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.