Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case

Abstract

In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some indications [arXiv:gr-qc/0611024] that Finsler geometry can provide some generalization of Riemannian geometry which may allow to account for non-trivial (Planckian) structure of relativistic particles' configuration space. We investigate the possibility to formalize Planck-scale deformations to relativistic models in curved spacetime, within the framework of Finsler geometry. We take into account the general strategy of analysis of modifications of dispersion relations in curved spacetimes proposed in [arXiv:1507.02056], generalizing to the de Sitter case the results obtained in [arXiv:1407.8143], for deformed relativistic particle kinematics in flat spacetime using Finsler formalism.

21 pages, 2 figures. Matches version published in PRD

References in corpus (10)

• Planck-scale modified dispersion relations and Finsler geometry
• Lorentz-violation-induced arrival delays of cosmological particles
• Realization of DSR-relativistic symmetries in Finsler geometries
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• Relativistic kinematics beyond Special Relativity
• Deformed relativity symmetries and the local structure of spacetime
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Lorentz Invariance Violation from String Theory
• Algebraic approach to quantum gravity II: noncommutative spacetime
• Exploring Special Relative Locality with deSitter momentum-space

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• Deformed relativistic kinematics on curved spacetime -- a geometric approach
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• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Modified particle lifetimes as a signature of deformed relativity
• Lorentz Violation in Finsler Geometry
• Space-time thermodynamics in momentum dependent geometries
• The extended phase space thermodynamics of Planck-scale-corrected Reissner-Nordström-anti-de Sitter black hole
• Revisiting Legendre transformations in Finsler geometry
• Muon accelerators -- Muon lifetime measurements as window to Planck scale physics
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• Universal Horizons without Hypersurface Orthogonality
• Finslerian geometrodynamics
• Experimental Bounds on Deformed Muon Lifetime Dilation