The Paneitz operator in 4D belongs to extended mimetic gravity and is constrained by gravitational wave propagation speed.
Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
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abstract
We propose a novel class of degenerate higher-order scalar-tensor theories as an extension of mimetic gravity. By performing a noninvertible conformal transformation on "seed" scalar-tensor theories which may be nondegenerate, we can generate a large class of theories with at most three physical degrees of freedom. We identify a general seed theory for which this is possible. Cosmological perturbations in these extended mimetic theories are also studied. It is shown that either of tensor or scalar perturbations is plagued with gradient instabilities, except for a special case where the scalar perturbations are presumably strongly coupled, or otherwise there appear ghost instabilities.
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Higher-derivative extension of dark matter yields an imperfect fluid that matches pressureless dust on homogeneous backgrounds but generates acceleration and vorticity to avoid caustic singularities in inhomogeneous cosmologies.
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Gravitational wave constraints on the Paneitz operator
The Paneitz operator in 4D belongs to extended mimetic gravity and is constrained by gravitational wave propagation speed.
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Imperfect dark matter with higher derivatives
Higher-derivative extension of dark matter yields an imperfect fluid that matches pressureless dust on homogeneous backgrounds but generates acceleration and vorticity to avoid caustic singularities in inhomogeneous cosmologies.