  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.
