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.

arXiv comment21 pages, 2 figures. Matches version published in PRD

References in corpus (34)

• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Quantum Spacetime Phenomenology
• Gravity's Rainbow
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• The principle of relative locality
• Lorentz violation and Crab synchrotron emission: a new constraint far beyond the Planck scale
• Planck-scale modified dispersion relations and Finsler geometry
• Quantum $\kappa$-Poincare in Any Dimensions
• Lorentz-violation-induced arrival delays of cosmological particles
• Taming nonlocality in theories with Planck-scale-deformed Lorentz symmetry
• Real Forms of Complex Quantum Anti de Sitter Algebra $U_q(Sp(4,C))$ and their Contraction Schemes
• Realization of DSR-relativistic symmetries in Finsler geometries
• Relative-locality distant observers and the phenomenology of momentum-space geometry
• Planck-scale-modified dispersion relations in FRW spacetime
• Dimensional reduction in the sky
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• IceCube and GRB neutrinos propagating in quantum spacetime
• Spacetime with zero point length is two-dimensional at the Planck scale
• Relativistic kinematics beyond Special Relativity
• Rainbow metric from quantum gravity
• Deformed relativity symmetries and the local structure of spacetime
• Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• Lorentz Invariance Violation from String Theory
• Dual redshift on Planck-scale-curved momentum spaces
• Extended disformal approach in the scenario of Rainbow Gravity
• Kinematics of particles with quantum de Sitter symmetries
• Algebraic approach to quantum gravity II: noncommutative spacetime
• Exploring Special Relative Locality with deSitter momentum-space
• Are we at the dawn of quantum-gravity phenomenology?
• On 3+1 anti-de Sitter and de Sitter Lie bialgebras with dimensionful deformation parameters
• Testing the wavelength dependence of cosmological redshift down to $\Delta z\sim 10^{-6}$
• Weakness of accelerator bounds on electron superluminality without a preferred frame

Cited by in corpus (29)

• Finsler gravity action from variational completion
• Curved spacetimes with local $\kappa$-Poincaré dispersion relation
• Deformed relativity symmetries and the local structure of spacetime
• Landau Levels in the Presence of a Cosmic String in Rainbow Gravity
• Reaching the Planck scale with muon lifetime measurements
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations
• Effects of Planck-scale-modified dispersion relations on the thermodynamics of charged black holes
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Does a deformation of special relativity imply energy dependent photon time delays?
• Black Hole Solutions with Constant Ricci Scalar in a Model of Finsler Gravity
• Rainbow-like Black Hole metric from Loop Quantum Gravity
• Quantum Configuration and Phase Spaces: Finsler and Hamilton Geometries
• Finsler gravitational waves of $(\alpha ,\beta )$-type and their observational signature
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry
• Modified particle lifetimes as a signature of deformed relativity
• Space-time thermodynamics in momentum dependent geometries
• Lorentz Violation in Finsler Geometry
• The extended phase space thermodynamics of Planck-scale-corrected Reissner-Nordström-anti-de Sitter black hole
• Physical velocity of particles in relativistic curved momentum space
• Black Holes Thermodynamics in a new kind of Noncommutative Geometry
• 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
• Remark on Remnant and Residue Entropy with GUP
• Universal Horizons without Hypersurface Orthogonality
• Experimental Bounds on Deformed Muon Lifetime Dilation
• Finslerian geometrodynamics