Covariant power-counting renormalizable gravity: Lorentz symmetry breaking and accelerating early-time FRW universe

We continue the study of covariant power-counting renormalizable gravity constrained by a scalar Lagrange multiplier. Lorentz-symmetry breaking is investigated in such a theory in comparison with the one in the 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 the covariant scalar/vector gravity under consideration may have a power-law or de Sitter accelerating cosmological solution corresponding to an inflationary era. The simplest black hole solution is obtained and dispersion relations for graviton are presented.