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.

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