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We investigate a large class of gravity theories that respect spatial covariance, and involve kinetic terms for both the spatial metric and the lapse function.
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D. Comelli, F. Nesti, and L. Pilo, Weak Massive Gravity
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D. Comelli, F. Nesti, and L. Pilo, Massive gravity: a General Analysis
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J. Gleyzes, D. Langlois, and F. Vernizzi, A unifying description of dark energy
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M. Crisostomi, K. Koyama, and G. Tasinato, Extended Scalar-Tensor Theories of Gravity
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D. Comelli, F. Nesti, and L. Pilo, Nonderivative Modified Gravity: a Classification
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2015
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R. P. Woodard, Ostrogradsky’s theorem on Hamiltonian instability
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R. Saitou, Canonical invariance of spatially covariant scalar-tensor theory
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H. Motohashi, T. Suyama, and K. Takahashi, Fundamental theorem on gauge fixing at the action level
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J. Chagoya and G. Tasinato, A geometrical approach to degenerate scalar-tensor theories
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