Planckscalemodified dispersion relations in FRW spacetime
Abstract
In recent years, Planckscale 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 Planckscale 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 propose here a general strategy of analysis of the effects of modifications of the dispersion relation in FriedmannRobertsonWalker spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled ("preferredframe scenarios") and to the alternative possibility of "DSRrelativistic theories," theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the JacobPiran ansatz implicitly assumes that spacetime translations are not affected by the Planck scale, while under rather general conditions, the same Planckscale quantumspacetime 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 Planckscale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.
 Publication:

Physical Review D
 Pub Date:
 December 2015
 DOI:
 10.1103/PhysRevD.92.124042
 arXiv:
 arXiv:1507.02056
 Bibcode:
 2015PhRvD..92l4042R
 Keywords:

 04.60.Bc;
 03.30.+p;
 98.80.Jk;
 Phenomenology of quantum gravity;
 Special relativity;
 Mathematical and relativistic aspects of cosmology;
 High Energy Physics  Theory;
 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology
 EPrint:
 Phys. Rev. D 92, 124042 (2015)