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Parameterizing dark sector perturbations via equations of state

The evolution of perturbations is a crucial part of the phenomenology of the dark sector cosmology. We advocate parameterizing these perturbations using equations of state for the entropy perturbation and the anisotropic stress. For small perturbations, these equations of state will be linear in the density, velocity and metric perturbations, and in principle these can be related back to the field content of the underlying model allowing for confrontation with observations. We illustrate our point by constructing gauge invariant entropy perturbations for theories where the dark sector Lagrangian is a general function of a scalar field, its first and second derivatives, and the metric and its first derivative, ${\cal L}={\cal L}(ϕ,\partial_μϕ,\partial_μ\partial_νϕ,g_{μν},\partial_αg_{μν})$. As an example, we show how to apply this approach to the case of models of Kinetic Gravity Braiding.