  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.
