  The Hamiltonian formulation of modified dispersion relations (MDRs) allows
for their implementation on generic curved spacetimes. In turn it is possible
to derive phenomenological effects. I will present how to construct the
kappa-Poincare dispersion relation on curved spacetimes, its spherically
symmetric realizations, among them the kappa deformation of Schwarzschild
spacetime, and its implementation on Friedmann-Lemaitre-Robertson-Walker
spacetimes with arbitrary scale factor. In addition we will construct the
general first order modifications of the general relativistic dispersion
relation. Afterwards we will use the perturbative MDRs to calculate specific
observables such as the redshift, lateshift and photon circular orbits.
