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We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made non-dynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in general relativity.
1905
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A. De Felice, A. Doll and S. Mukohyama, A theory of type-II minimally modified gravity , JCAP 09
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X. Gao, Hamiltonian analysis of spatially covariant gravity , Phys. Rev. D 90
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M. Crisostomi, K. Koyama and G. Tasinato, Extended Scalar-Tensor Theories of Gravity , JCAP 04
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