We consider a model where a light scalar field (with mass $lesssim 30, {rm eV}$), conjectured to be dark matter, has a non-minimal coupling to gravity. In the non-relativistic limit, this new coupling introduces a self-interaction term in the scalar-field equation of motion, and modifies the source term for the gravitational field. Moreover, in the small-coupling limit justified by the observed dark-matter density, the system further reduces to the Gross-Pitaevskii-Poisson equations, which remarkably also arise from a self-gravitating and self-interacting Bose-Einstein condensate system. We derive predictions of our model on linear and non-linear structure formation by exploiting this unexpected connection.
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