  We continue the study of covariant power-counting renormalizable gravity
constrained by scalar Lagrange multiplier. Lorentz symmetry breaking is
investigated in such a theory in comparison with the one in ghost condensation
model. Covariant power-counting renormalizable vector gravity which is
invariant under $U(1)$ gauge symmetry is proposed. Several forms of vector
Lagrange multiplier in this theory are discussed. It is shown that covariant
scalar/vector gravity under consideration may have power-law or de Sitter
accelerating cosmological solution corresponding to inflationary era. Simplest
black hole solution is obtained and dispersion relations for graviton are
presented.
