Modified dispersion relations in extra dimensions

TL;DR

This paper derives the form of Modified Dispersion Relations (MDR) in extra dimensions by analyzing the thermodynamics of a FRW universe, showing their potential equivalence to GUP-based approaches and implications for quantum gravity theories.

Contribution

It introduces a method to derive MDR in extra dimensions using FRW thermodynamics, establishing a link with GUP-based approaches and advancing quantum gravity models.

Findings

Entropy functionals from MDR and GUP approaches are identical.

Derived MDR form in extra dimensions consistent with thermodynamic analysis.

Results suggest MDR and GUP approaches may be equivalent in extra-dimensional theories.

Abstract

It has recently been shown that the thermodynamics of a FRW universe can be fully derived using the generalized uncertainty principle (GUP) in extra dimensions as a primary input. There is a phenomenologically close relation between the GUP and Modified Dispersion Relations (MDR). However, the form of the MDR in theories with extra dimensions is as yet not known. The purpose of this letter is to derive the MDR in extra dimensional scenarios. To achieve this goal, we focus our attention on the thermodynamics of a FRW universe within a proposed MDR in an extra dimensional model universe. We then compare our results with the well-known results for the thermodynamics of a FRW universe in an extra dimensional GUP setup. The result shows that the entropy functionals calculated in these two approaches are the same, pointing to a possible conclusion that these approaches are equivalent. In this way, we derive the MDR form in a model universe with extra dimensions that would have interesting implications on the construction of the ultimate quantum gravity scenario.