Imperfect dark matter with higher derivatives

TL;DR

This work introduces a higher-derivative generalization of mimetic gravity to model dark matter as an imperfect fluid whose EMT contains nonzero pressure, energy flux, and anisotropic stress. The authors derive a generalized mimetic constraint $X f\left(\tfrac{Y}{X^2}, \tfrac{Z}{X^3}\right)=1$ from a systematic singular-disformal framework, showing how second- and third-derivative structures can be incorporated without Ostrogradsky ghosts. On homogeneous backgrounds the model reproduces dust dynamics, but in the presence of inhomogeneities it generates nonzero acceleration and vorticity, feeding into the Raychaudhuri equation to counteract geodesic focusing and potentially avoid caustics. The approach provides a ghost-free, analytically tractable route to alleviate mimetic dark matter caustic pathologies while enriching phenomenology for structure formation.

Abstract

We introduce a higher-derivative action for dark matter whose energy-momentum tensor describes an imperfect fluid with nonzero pressure, energy flux, and anisotropic stress. In the limit where the higher-derivative couplings are switched off, the energy-momentum tensor reduces to pressureless dust. A systematic derivation follows from extending the singular conformal transformation used in the mimetic dark matter scenario to include higher-derivative terms while the resulting action is general and does not rely on the mimetic framework. On a homogeneous cosmological background, the dynamics coincides with that of pressureless dust, while in the presence of inhomogeneities the higher-derivative terms generate nonzero acceleration and vorticity, making it possible to avoid the formation of caustic singularities even if the strong energy condition satisfies. In particular, within the mimetic realization these terms resolve the usual caustic pathology of mimetic dark matter.