A new covariant foliation-based construction of scalar-tensor theories up to four derivatives of the scalar field that extends DHOST and U-DHOST without unitary gauge and propagates three degrees of freedom.
Gao,Unifying framework for scalar-tensor theories of gravity, Phys
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Five explicit polynomial spatially covariant gravity Lagrangians up to total derivative order three are identified that propagate only two degrees of freedom up to cubic order in perturbations around a cosmological background.
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Covariant scalar-tensor theories beyond second derivatives
A new covariant foliation-based construction of scalar-tensor theories up to four derivatives of the scalar field that extends DHOST and U-DHOST without unitary gauge and propagates three degrees of freedom.
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Spatially covariant gravity with two degrees of freedom: A perturbative analysis up to cubic order
Five explicit polynomial spatially covariant gravity Lagrangians up to total derivative order three are identified that propagate only two degrees of freedom up to cubic order in perturbations around a cosmological background.