The low-energy dynamics of a generic self-gravitating medium can be studied by using effective field theory (EFT) in terms of four derivatively coupled scalar fields. Imposing SO(3) internal spatial invariance, the theory describes fluids, superfluids, solids and supersolids. Dynamical and thermodynamical properties of the medium are dictated by internal symmetries of the effective theory. From the analysis of cosmological perturbations it emerges that in the scalar sector, besides the gravitational potential, there is a non-adiabatic mode corresponding to the perturbations of the entropy per particle σ. Perfect fluids and solids are adiabatic with σ constant in time, while for superfluids and supersolids σ has non-trivial dynamics. Tensor perturbations are massive for solids and supersolids. Such an effective approach can be used to give a very general modelling of the dark sector based on symmetries.
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