  We propose several covariant models which may solve one of the problems in
the cosmological constant. One of the model can be regarded as an extension of
sequestering model. Other models could be regarded as extensions of the
covariant formulation of the unimodular gravity. The contributions to the
vacuum energy from the quantum corrections from the matters are absorbed into a
redefinition of a scalar field and the quantum corrections become irrelevant to
the dynamics. In a class of the extended unimodular gravity models, we also
consider models which are regarded as topological field theories. The models
can be extended and not only the vacuum energy but any quantum corrections to
the gravitational action could become irrelevant for the dynamics. We find,
however, that the BRS symmetry in the topological field theories is broken
spontaneously and therefore the models might not be consistent.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology