Abstract: In this talk, a modified gravity theory with diffeomorphism breaking using nondynamical background fields is presented. In particular, we focus on the Ricci coupling and scalar sectors of the gravitational Standard-Model Extension (SME). We perform the Hamiltonian formulation and provide an extension of the Gibbons-Hawking-York (GHY) boundary term. We also show the equivalence of both constraints and dynamics of the induced three metric on the hypersurface in the Lagrangian and Hamiltonian formalisms. At the end we comment on some cosmological studies on the late time acceleration of the universe and possible applications in black hole physics.

 Acknowledgements

This event is part of the grant CEX2019-000918-M funded by MCIN/AEI/10.13039/501100011033.