Does a deformation of special relativity imply energy dependent photon time delays?

Theoretical arguments in favor of energy dependent photon time delays from a modification of special relativity (SR) have met with recent gamma ray observations that put severe constraints on the scale of such deviations. We review the case of the generality of this theoretical prediction in the case of a deformation of SR and find that, at least in the simple model based on the analysis of photon worldlines which is commonly considered, there are many scenarios compatible with a relativity principle which do not contain a photon time delay. This will be the situation for any modified dispersion relation which reduces to E=|p⃗ | for photons, independently of the quantum structure of spacetime. This fact opens up the possibility of a phenomenologically consistent relativistic generalization of SR with a new mass scale many orders of magnitude below the Planck mass

Relativistic deformed kinematics from momentum space geometry

We present a way to derive a deformation of special relativistic kinematics (possible low-energy signal of a quantum theory of gravity) from the geometry of a maximally symmetric curved momentum space. The deformed kinematics is fixed (up to change of coordinates in the momentum variables) by the algebra of isometries of the metric in momentum space. In particular, the well-known example of ¿-Poincaré kinematics is obtained when one considers an isotropic metric in de Sitter momentum space such that translations are a subgroup of the isometry group, and for a Lorentz covariant algebra one gets the also well-known case of Snyder kinematics. We prove that our construction gives generically a relativistic kinematics and explain how it relates to previous attempts of connecting a deformed kinematics with a geometry in momentum space

Does a deformation of special relativity imply energy dependent photon time delays?

Theoretical arguments in favor of energy dependent photon time delays from a modification of special relativity (SR) have met with recent gamma ray observations that put severe constraints on the scale of such deviations. We review the case of the generality of this theoretical prediction in the case of a deformation of SR and find that, at least in the simple model based on the analysis of photon worldlines which is commonly considered, there are many scenarios compatible with a relativity principle which do not contain a photon time delay. This will be the situation for any modified dispersion relation which reduces to E = |p¿| for photons, independently of the quantum structure of spacetime. This fact opens up the possibility of a phenomenologically consistent relativistic generalization of SR with a new mass scale many orders of magnitude below the Planck mass

Relativistic deformed kinematics from locality conditions in a generalized spacetime

We show how a deformed composition law of four-momenta can be used to define, at the classical level, a modified notion of spacetime for a system of two particles through the crossing of worldlines in particle interactions. We present a derivation of a generic relativistic isotropic deformed kinematics and discuss the complementarity and relations with other derivations based on kappa-Poincare Hopf algebra or on the geometry of a maximally symmetric momentum space

Time delays, choice of energy-momentum variables, and relative locality in doubly special relativity

Doubly special relativity (DSR) theories consider (quantum-gravity motivated) deformations of the symmetries of special relativity compatible with a relativity principle. The existence of time delays for massless particles, one of their proposed phenomenological consequences, is a delicate question since, contrary to what happens with Lorentz invariance violation scenarios, they are not simply determined by the modification in the particle dispersion relation. While some studies of DSR assert the existence of photon time delays, in this paper we generalize a recently proposed model for time delay studies in DSR and show that the existence of photon time delays does not necessarily follow from a DSR scenario, determining in which cases this is so. Moreover, we clarify long-standing questions about the arbitrariness in the choice of the energy-momentum labels and the independence of the time delay on this choice, as well as on the consistency of its calculation with the relative locality paradigm of DSR theories. Finally, we show that the result for time delays is reproduced in models that consider propagation in a noncommutative spacetime

Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency

We analyze the kinematics of electron-positron production in a photon-photon interaction when one has a modification of the special relativistic kinematics as a power expansion in the inverse of a new high-energy scale. We derive the equation for the threshold energy of this reaction to first order in this expansion, including the effects due to a modification of the energy-momentum conservation equation. In contrast with the Lorentz invariance violation case, a scale of the order of a few TeV is found to be compatible with the observations of very high-energy cosmic gamma rays in the case of a modification compatible with the relativity principle

Particle–antiparticle asymmetry in relativistic deformed kinematics

Relativistic deformed kinematics are usually considered a way to capture the residual effects of a fundamental quantum gravity theory. These kinematics present a non-commutative addition law for the momenta so that the total momentum of a multi-particle system depends on the specific ordering in which the momenta are composed. We explore in the present work how this property may be used to generate an asymmetry between particles and antiparticles through a particular ordering prescription, resulting in a violation of CPT symmetry. We study its consequences for muon decay, obtaining a difference in the lifetimes of the particle and the antiparticle as a function of the new high-energy scale, parameterizing such relativistic deformed kinematics. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Modification of the mean free path of very high-energy photons due to a relativistic deformed kinematics

Ultra-high-energy physics is about to enter a new era thanks to the impressive results of experiments such as the Large High Altitude Air Shower Observatory, detecting photons of up to 1.4×10^15 eV (PeV scale). These new results could be used to test deviations with respect to special relativity. While this has been already explored within the approach of Lorentz Invariance Violation theories, in this work we consider, for the first time, modifications due to a relativistic deformed kinematics (which appear in Doubly Special Relativity, or DSR, theories). In particular, we study the mean free path of very high-energy photons due to electron-positron pair creation when interacting with low-energy photons of the cosmic microwave background. Depending on the energy scale of the relativistic deformed kinematics, present (or near future) experiments can be sensitive enough to be able to identify deviations from special relativity

Effects of new physics in neutrino propagation

In this work we consider the effects of Lorentz Invariance Violation over the observed flux of very high-energy neutrinos. For that, we study the neutrino propagation in a Modified Dispersion Relation scenario with a superluminal velocity. This makes the neutrino unstable and causes a cut-off in the flux of detected neutrinos. Using simple models, one can approximate the location of the cut-off as functions of the parameters of new physics and the closest source

Physics of the universe transparency in a deformed kinematics

We present a first study of the possible effects of a relativistic deformation of special relativity in the recent observations of very high-energy gamma rays by the LHAASO experiment, which has opened a new phenomenological window to study deformations in the kinematics of special relativity. Our analysis of the interaction of high-energy photons with the CMB background complements theoretical studies based on Lorentz invariance violation scenarios, while making predictions that would allow one to distinguish between a violation and a deformation of the symmetries of special relativity