Constraints on the deformation scale of a geometry in the cotangent bundle

Abstract

There are several studies proposing phenomenological consequences of a deformation of special and general relativity. Here, we cast novel constraints on the deformation parameter of a metric in the cotangent bundle accounting for a curved momentum space. In an expanding universe, we study three possible observations that could restrict our model, focusing on the deformations of velocity, redshift and luminosity distance, which in the aforementioned framework, depend on the energy of the particles. We find that for an energy dependent velocity there would be no time delay for massless particles since also the observed distance to the source depends on the energy. For the redshift and luminosity distance we see that a scale of the order of some keV could be compatible with our model. This shows that the constraints on the high-energy scale parametrizing the momentum dependent deviation from a Friedmann-Robertson-Walker metric are at the moment weak due to the fact that the precision (rather than energies) needed in the observational constraints are extremely high. However, this is not the case when considering the synchrotron radiation. Indeed, the observation of such emission from the Crab Nebula, for deformations leading to subluminal propagation at high energies, leads to a constraint for the high-energy scale of the order of 1 PeV.

11 pages

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Cited by in corpus (11)

• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Schwarzschild-Finsler-Randers spacetime: Dynamical analysis, Geodesics and Deflection Angle
• Applications of the Schwarzschild-Finsler-Randers model
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Modification of the mean free path of very high energy photons due to a relativistic deformed kinematics
• Time delays, choice of energy-momentum variables and relative locality in doubly special relativity
• Space-time thermodynamics in momentum dependent geometries
• Relativistic deformed kinematics: from flat to curved spacetimes
• Cosmic Neutrinos as a Window to Departures from Special Relativity
• Exploring black hole mechanics in cotangent bundle geometries