Material models of dark energy

Abstract

We review and develop a new class of "dark energy" models, in which the relativistic theory of solids is used to construct material models of dark energy. These are models which include the effects of a continuous medium with well defined physical properties at the level of linearized perturbations. The formalism is constructed for a medium with arbitrary symmetry, and then specialised to isotropic media (which will be the case of interest for the majority of cosmological applications). We develop the theory of relativistic isotropic viscoelastic media whilst keeping in mind that we ultimately want to observationally constrain the allowed properties of the material model. We do this by obtaining the viscoelastic equations of state for perturbations (the entropy and anisotropic stress), as well as identifying the consistent corner of the theory which has constant equation of state parameter $\dot{w}=0$. We also connect to the non-relativistic theory of solids, by identifying the two quadratic invariants that are needed to construct the energy-momentum tensor, namely the Rayleigh dissipation function and Lagrangian for perturbations. Finally, we develop the notion that the viscoelastic behavior of the medium can be thought of as a non-minimally coupled massive gravity theory. This also provides a tool-kit for constructing consistent generalizations of coupled dark energy theories.