Constraints on the deformation scale of a geometry in the cotangent bundle

There are several studies proposing phenomenological consequences of a deformation of special and general relativity. Here, we cast novel constraints on the deformation parameter of a metric in the cotangent bundle accounting for a curved momentum space. In an expanding universe, we study three possible observations that could restrict our model, focusing on the deformations of velocity, redshift and luminosity distance, which in the aforementioned framework, depend on the energy of the particles. We find that for an energy dependent velocity there would be no time delay for massless particles since also the observed distance to the source depends on the energy. For the redshift and luminosity distance we see that a scale of the order of some keV could be compatible with our model. This shows that the constraints on the high-energy scale parametrizing the momentum dependent deviation from a Friedmann-Robertson-Walker metric are at the moment weak due to the fact that the precision (rather than energies) needed in the observational constraints are extremely high. However, this is not the case when considering the synchrotron radiation. Indeed, the observation of such emission from the Crab Nebula, for deformations leading to subluminal propagation at high energies, leads to a constraint for the high-energy scale of the order of 1 PeV.