Emergence of a Dark Force in Corpuscular Gravity

Abstract: We investigate the emergent laws of gravity when Dark Energy and the de Sitter space-time are modelled as a critical Bose-Einstein condensate of a large number of soft gravitons $N_{\rm G}$. We argue that this scenario requires the presence of various regimes of gravity in which $N_{\rm G}$ scales in different ways. Moreover, the local gravitational interaction affecting baryonic matter can be naturally described in terms of gravitons pulled out from this Dark Energy condensate (DEC). We then explain the additional component of the acceleration at galactic scales, commonly attributed to dark matter, as the reaction of the DEC to the presence of baryonic matter. This additional dark force is also associated to gravitons pulled out from the DEC and correctly reproduces the MOND acceleration. It also allows for an effective description in terms of General Relativity sourced by an anisotropic fluid. We finally calculate the mass ratio between the contribution of the apparent dark matter and the baryonic matter in a region of size $r$ at galactic scales and show that it is consistent with the $\Lambda$CDM predictions.