Planck-scale-modified dispersion relations in FRW spacetime

TL;DR

This paper develops a general framework to analyze how Planck-scale modifications of dispersion relations influence cosmological spacetimes, especially in non-constant curvature scenarios, revealing potential observable effects like quantum corrections to travel times.

Contribution

It introduces a comprehensive strategy for studying Planck-scale effects in FRW spacetimes, extending beyond the Jacob-Piran ansatz to include effects on spacetime translations and their observable consequences.

Findings

Planck-scale effects can alter spacetime translations.

Modified dispersion relations lead to measurable quantum corrections in travel times.

The proposed framework applies to both preferred-frame and DSR-relativistic scenarios.

Abstract

In recent years Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We here propose a general strategy of analysis of the effects of modifications of dispersion relation in FRW spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled ("preferred-frame scenarios") and to the alternative possibility of "DSR-relativistic theories", theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the Jacob-Piran ansatz implicitly assumes that spacetime translations are not affected by the Planck-scale, while under rather general conditions the same Planck-scale quantum-spacetime structures producing modifications of the dispersion relation also affect translations. Through the explicit analysis of one of the effects produced by modifications of the dispersion relation, an effect amounting to Planck-scale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.