Lorentz Invariance Violation effects on UHECR propagation: A geometrized approach

Abstract

We explore the possibility to geometrize the interaction of massive fermions with the quantum structure of space-time, trying to create a theoretical background, in order to explain what some recent experimental results seem to implicate on the propagation of Ultra High Energy Cosmic Rays (UHECR). We will investigate part of the phenomenological implications of this approach on the predicted effect of the UHECR suppression, in fact recent evidences seem to involve the modification of the GZK cut-off phenomenon. The search for an effective theory, which can explain this physical effect, is based on Lorentz Invariance Violation (LIV), which is introduced via Modified Dispersion Relations (MDRs). Furthermore we illustrate that this perspective implies a more general geometry of space-time than the usual Riemannian one, indicating, for example, the opportunity to resort to Finsler theory.

Neutrino oscillations and Lorentz invariance violation in a Finslerian geometrical model

“…A significant numbers of these tests has to do with the study of neutrino properties, also because neutrino phenomenology is extremely reach and spans over a very wide range of energies. In this paper we consider a class of models, more widely discussed in [7], in which the possibility of LIV is introduced starting from a modified version of dispersion relations and is founded on a more general geometrical description, making use of Finsler geometry. The choice of the particular form of the terms violating Lorentz Invariance, represented as an homogeneous function of | − → p | E , guarantees the possibility of preserving a metric structure and, moreover, the LIV corrections are chosen in such a way to Figure 9: Percentage variations induced in the neutrino oscillation probabilities by the LIV corrections.…”

Homogeneously Modified Special relativity (HMSR)

“…This approach consists in modifying the dispersion relations describing the free particle propagation. The Dispersion Relations of standard physics, written using the Minkowski metric as E 2 − | − → p | 2 = m 2 ⇒ p μ η μν p ν = m 2 , are modified, following [24,25], to a more general case of Modified Dispersion Relations (MDR):…”

“…The perturbation form introduced in this work can be justified because it is, for example, a subcase obtained in [3], so it constitutes an interesting physical eventuality per se. Moreover, it is possible to demonstrate that every Modified Dispersion Relation of the form (5) can be approximated with a MDR of type (4), as in [24,25]. In fact, perturbation function f , that preserves rotational symmetry can be rewritten in the form:…”

“…It remains a non-diagonal part, which does not give any contribution in computing the dispersion relations. Therefore it can be eliminated by an opportune "gauge" choice [24]. The final form of the metric becomes therefore:…”

“…Following [24] and [25], it is simple to evaluate the explicit forms of the affine connection components, starting from the metric tensor. The result is identically equal to zero for the following Christoffel symbols:…”