A Born-Infeld action for dark matter and dark energy

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We consider a Born-Infeld like action for gravity coupled to an external connection field. We show that the equation of state of this fluid interpolates between dark matter and dark energy. We also show that on galactic scales this system predicts asymptotically flat rotation curves. This action is motivated by looking at a regime where the metric vanishes, and replacing the big bang by a smooth transition between a topological manifold to a Riemannian manifold.