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In recent years, Planck-scale modifications to particles' dispersion relationhave been deeply studied for the possibility to formulate some phenomenology ofPlanckian effects in astrophysical and cosmological frameworks. There are someindications [arXiv:gr-qc/0611024] that Finsler geometry can provide somegeneralization of Riemannian geometry which may allow to account fornon-trivial (Planckian) structure of relativistic particles' configurationspace. We investigate the possibility to formalize Planck-scale deformations torelativistic models in curved spacetime, within the framework of Finslergeometry. We take into account the general strategy of analysis ofmodifications 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 flatspacetime using Finsler formalism.

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