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

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.

12 pages, 5 figures

References in corpus (5)

• Probing quantum gravity using photons from a flare of the active galactic nucleus Markarian 501 observed by the MAGIC telescope
• Lorentz-violation-induced arrival delays of cosmological particles
• Prospects for constraining quantum gravity dispersion with near term observations
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• Special Relativity in the 21${}^{\mathrm{st}}$ century

Cited by in corpus (5)

• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• Curved momentum spaces from quantum groups with cosmological constant
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant