Consistent perturbations in an imperfect fluid

Abstract

We present a new prescription for analysing cosmological perturbationsin a more-general class of scalar-field dark-energy models where theenergy-momentum tensor has an imperfect-fluid form. This class includesBrans-Dicke models, f(R) gravity, theories with kinetic gravitybraiding and generalised galileons. We employ the intuitive languageof fluids, allowing us to explicitly maintain a dependence on physicaland potentially measurable properties. We demonstrate that hydrodynamicsis not always a valid description for describing cosmological perturbationsin general scalar-field theories and present a consistent alternativethat nonetheless utilises the fluid language.We apply this approach explicitly to a worked example: k-essencenon-minimally coupled to gravity. This is the simplest case whichcaptures the essential new features of these imperfect-fluid models.We demonstrate the generic existence of a new scale separating regimeswhere the fluid is perfect and imperfect. We obtain the equationsfor the evolution of dark-energy density perturbations in both theseregimes. The model also features two other known scales: the Comptonscale related to the breaking of shift symmetry and the Jeans scalewhich we show is determined by the speed of propagation of small scalar-fieldperturbations, i.e. causality, as opposed to the frequently used definitionof the ratio of the pressure and energy-density perturbations.