Effective Fluid Description of the Dark Universe

Abstract: We propose an effective anisotropic fluid description for a generic infrared-modified theory of gravity. In our framework, the additional component of the acceleration, commonly attributed to dark matter, is explained as a radial pressure generated by the reaction of the dark energy fluid to the presence of baryonic matter. Using quite general assumptions, and a microscopic description of the fluid in terms of a Bose-Einstein condensate of gravitons, we find the static, spherically symmetric solution for the metric in terms of the Misner-Sharp mass function and the fluid pressure. At galactic scales, we correctly reproduce the leading MOND-like $\log(r)$ and subleading $(1/r)\,\log(r)$ terms in the weak-field expansion of the potential. Our description also predicts a tiny (of order $10<sup>{-6}$ for a typical spiral galaxy) Machian modification of the Newtonian potential at galactic scales, which is controlled by the cosmological acceleration.