Generalized boundary conditions in closed cosmologies

Considering a generalization of the Gibbons-Hawking-York covariant boundary action that depends on both the extrinsic and the intrinsic geometry of the boundary, we derive boundary conditions for the cosmological background and tensor perturbations in a closed universe with space-like boundaries. We also give a general method to reconstruct the covariant boundary action starting from a given set of boundary conditions for the cosmological background. These results may be of special relevance in the context of the path-integral formulation of quantum cosmology, where boundary terms contain essential physical information of the system.