Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes

Abstract

The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lemaître-Robertson-Walker (FLRW) geometry that is locally identical to the $\kappa$-Poincaré dispersion relation, in the same way as the dispersion relation of point particles in general relativity is locally identical to the one valid in special relativity. Studying the motion of particles subject to such Hamiltonian we derive the redshift and lateshift as observable consequences of the Planck-scale deformed FLRW universe.

References in corpus (6)

• Lorentz-violation-induced arrival delays of cosmological particles
• Prospects for constraining quantum gravity dispersion with near term observations
• Light speed variation from gamma ray burst GRB 160509A
• Probing a Possible Vacuum Refractive Index with Gamma-Ray Telescopes
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
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