Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime

TL;DR

This paper develops a model of deformed Lorentz symmetry in a curved, expanding spacetime, specifically de Sitter space, incorporating three key relativistic invariants and addressing previous limitations of flat spacetime models.

Contribution

It provides the first explicit example of a relativistic particle theory with deformed Lorentz symmetry in a curved, expanding spacetime, advancing understanding of quantum gravity effects in cosmological contexts.

Findings

First example of deformed Lorentz symmetry in de Sitter spacetime

Incorporates speed-of-light, expansion-rate, and Planck scales as invariants

Addresses challenges of previous flat spacetime models

Abstract

The interest of part of the quantum-gravity community in the possibility of Planck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale ("speed-of-light scale"), a large distance scale (inverse of the "expansion-rate scale"), and a large momentum scale ("Planck scale"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.