doi:10.1103/PhysRevD.101.064062engRelancio, J.J.Liberati, S.Phenomenological consequences of a geometry in the cotangent bundleART-2020-117883A deformed relativistic kinematics can be understood within a geometrical framework through a maximally symmetric momentum space. However, when considering this kind of approach, usually one works in a flat spacetime and in a curved momentum space. In this paper, we will discuss a possible generalization to take into account both curvatures and some possible observable effects. We will first explain how to construct a metric in the cotangent bundle in order to have a curved spacetime with a nontrivial geometry in momentum space and the relationship with an action in phase space characterized by a deformed Casimir. Then, we will study within this proposal two different space-time geometries. In the Friedmann-Robertson-Walker universe, we will see the modifications in the geodesics (redshift, luminosity distance, and geodesic expansion) due to a momentum dependence of the metric in the cotangent bundle. Also, we will see that when the spacetime considered is a Schwarzschild black hole, one still has a common horizon for particles with different energies, differently from a Lorentz invariance violation case. However, the surface gravity computed as the peeling off of null geodesics is energy dependent.2020http://zaguan.unizar.es/record/8977410.1103/PhysRevD.101.064062http://zaguan.unizar.es/record/89774oai:zaguan.unizar.es:89774info:eu-repo/grantAgreement/EUR/COST-Action/CA18108info:eu-repo/grantAgreement/ES/DGIID-DGA/2015-E24-2info:eu-repo/grantAgreement/ES/MINECO-FEDER/PGC2018-095328-B-I00Physical Review D 101, 6 (2020), 064062 1-15All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess