Rainbow metric formalism and Relative Locality

This proceeding is based on a talk prepared for the XIII Marcell Grossmann meeting. We summarise some results of work in progress in collaboration with Giovanni Amelino-Camelia about momentum dependent (Rainbow) metrics in a Relative Locality framework and we show that this formalism is equivalent to the Hamiltonian formalization of Relative Locality obtained in arXiv:1102.4637.Comment: appears in Proceedings of the 13th Marcell Grossmann meeting on General Relativity, World Scientific, Singapore, (2014

Quantum Gravity phenomenology and metric formalism

In this proceedings for the MG14 conference, we discuss the construction of a phenomenology of Planck-scale effects in curved spacetimes, underline a few open issues and describe some perspectives for the future of this research line

Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations

Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with Modified Dispersion Relation. In this paper, we introduce the reader to some realizations of this general idea: the original Rainbow metrics proposal, the momentum-space-inspired metric, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.Comment: 10 pages. Discussion on the role of connections was added. Matches published versio

Dual redshift on Planck-scale-curved momentum spaces

Several approaches to the investigation of the quantum-gravity problem have provided "theoretical evidence" of a role for the Planck scale in characterizing the geometry of momentum space. One of the main obstructions for a full exploitation of this scenario is the understanding of the role of the Planck-scale-curved geometry of momentum space in the correlations between emission and detection times, the "travel times" for a particle to go from a given emitter to a given detector. These travel times appear to receive Planck-scale corrections for which no standard interpretation is applicable, and the associated implications for spacetime locality gave rise to the notion of "relative locality" which is still in the early stages of investigation. We here show that these Planck-scale corrections to travel times can be described as "dual redshift" (or "lateshift"): they are manifestations of momentum-space curvature of the same type already known for ordinary redshift produced by spacetime curvature. In turn we can identify the novel notion of "relative momentum-space locality" as a known but under-appreciated feature associated to ordinary redshift produced by spacetime curvature, and this can be described in complete analogy with the relative spacetime locality that became of interest in the recent quantum-gravity literature. We also briefly comment on how these findings may be relevant for an approach to the quantum-gravity problem proposed by Max Born in 1938 and centered on Born duality.Comment: 13 pages, LaTe

In-vacuo-dispersion features for GRB neutrinos and photons

Over the last 15 years there has been considerable interest in the possibility of quantum-gravity-induced in-vacuo dispersion, the possibility that spacetime itself might behave essentially like a dispersive medium for particle propagation. Two very recent studies have exposed what might be in-vacuo dispersion features for GRB (gamma-ray-burst) neutrinos of energy in the range of 100 TeV and for GRB photons with energy in the range of 10 GeV. We here show that these two features are roughly compatible with a description such that the same effects apply over 4 orders of magnitude in energy. We also characterize quantitatively how rare it would be for such features to arise accidentally, as a result of (still unknown) aspects of the mechanisms producing photons at GRBs or as a result of background neutrinos accidentally fitting the profile of a GRB neutrino affected by in-vacuo dispersion.Comment: 12 pages, latex. arXiv admin note: text overlap with arXiv:1609.0398

Hamilton geometry: Phase space geometry from modified dispersion relations

We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\kappa$-Poincar\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.Comment: 32 pages, section on quantisation of the theory added, comments on additin of momenta on curved momentum spaces extende

Quantum-gravity-induced dual lensing and IceCube neutrinos

Momentum-space curvature, which is expected in some approaches to the quantum-gravity problem, can produce dual redshift, a feature which introduces energy dependence of the travel times of ultrarelativistic particles, and dual lensing, a feature which mainly affects the direction of observation of particles. In our recent arXiv:1605.00496 we explored the possibility that dual redshift might be relevant in the analysis of IceCube neutrinos, obtaining results which are preliminarily encouraging. Here we explore the possibility that also dual lensing might play a role in the analysis of IceCube neutrinos. In doing so we also investigate issues which are of broader interest, such as the possibility of estimating the contribution by background neutrinos and some noteworthy differences between candidate "early neutrinos" and candidate "late neutrinos".Comment: In this version V2 we give a definition of variation probability which could be considered in alternative to the notion of variation probability already introduced in version V1; both notions of variation probability are contemplated in the data analysis. arXiv admin note: text overlap with arXiv:1605.0049

Hamilton Geometry - Phase Space Geometry from Modified Dispersion Relations

Quantum gravity phenomenology suggests an effective modification of the general relativistic dispersion relation of freely falling point particles caused by an underlying theory of quantum gravity. Here we analyse the consequences of modifications of the general relativistic dispersion on the geometry of spacetime in the language of Hamilton geometry. The dispersion relation is interpreted as the Hamiltonian which determines the motion of point particles. It is a function on the cotangent bundle of spacetime, i.e. on phase space, and determines the geometry of phase space completely, in a similar way as the metric determines the geometry of spacetime in general relativity. After a review of the general Hamilton geometry of phase space we discuss two examples. The phase space geometry of the metric Hamiltonian $H_g(x,p)=g^{ab}(x)p_ap_b$ and the phase space geometry of the first order q-de Sitter dispersion relation of the form $H_{qDS}(x,p)=g^{ab}(x)p_ap_b + \ell G^{abc}(x)p_ap_bp_c$ which is suggested from quantum gravity phenomenology. We will see that for the metric Hamiltonian $H_g$ the geometry of phase space is equivalent to the standard metric spacetime geometry from general relativity. For the q-de Sitter Hamiltonian $H_{qDS}$ the Hamilton equations of motion for point particles do not become autoparallels but contain a force term, the momentum space part of phase space is curved and the curvature of spacetime becomes momentum dependent.Comment: 6 page