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

Over the last few years, Planck-scale modifications to the dispersion relation of particles have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some indications F. Girelli, S. Liberati, and L. Sindoni, Phys. Rev. D 75, 064015 (2007) that Finsler geometry can provide some generalization of Riemannian geometry which may allow us to account for the nontrivial (Planckian) structure of the 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 dispersion relations modifications in curved spacetimes proposed in G. Rosati, G. Amelino-Camelia, A. Marciano, and M. Matassa, Phys. Rev. D 92, 124042 (2015), generalizing to the de Sitter case the results obtained in G. Amelino-Camelia, L. Barcaroli, G. Gubitosi, S. Liberati, and N. Loret, Phys. Rev. D 90, 125030 (2014) for deformed relativistic particle kinematics in flat spacetime using Finsler formalism.