Consistent perturbations in an imperfect fluid

Abstract: We present a new prescription for analysing cosmological perturbations in a more-general class of scalar-field dark-energy models where the energy-momentum tensor has an imperfect-fluid form. This class includes Brans-Dicke models, f(R) gravity, theories with kinetic gravity braiding and generalised galileons. We employ the intuitive language of fluids, allowing us to explicitly maintain a dependence on physical and potentially measurable properties. We demonstrate that hydrodynamics is not always a valid description for describing cosmological perturbations in general scalar-field theories and present a consistent alternative that nonetheless utilises the fluid language. We apply this approach explicitly to a worked example: k-essence non-minimally coupled to gravity. This is the simplest case which captures the essential new features of these imperfect-fluid models. We demonstrate the generic existence of a new scale separating regimes where the fluid is perfect and imperfect. We obtain the equations for the evolution of dark-energy density perturbations in both these regimes. The model also features two other known scales: the Compton scale related to the breaking of shift symmetry and the Jeans scale which we show is determined by the speed of propagation of small scalar-field perturbations, i.e. causality, as opposed to the frequently used definition of the ratio of the pressure and energy-density perturbations.