Observables from modified dispersion relations on curved spacetimes:circular orbits, redshift and lateshift

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.