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We study the cosmological stability of a class of theories with a dynamical preferred frame. For a range of actions, we find cosmological solutions which are compatible with observations of the recent history of the Universe: a matter-dominated era followed by accelerated expansion. We then study the evolution of linear perturbations on these backgrounds and find conditions on the parameters of the theory which allow for the growth of structure sourced by the new degrees of freedom.
Złośnik et al. (Mon,) studied this question.