Gravitational forces from Bose-Einstein condensation

Abstract

The basic idea that gravity can be a long-wavelength effect {\it induced} by the peculiar ground state of an underlying quantum field theory leads to consider the implications of spontaneous symmetry breaking through an elementary scalar field. We point out that Bose-Einstein condensation implies the existence of long-range order and of a gap-less mode of the (singlet) Higgs-field. This gives rise to a $1/r$ potential and couples with infinitesimal strength to the inertial mass of known particles. If this is interpreted as the origin of Newtonian gravity one finds a natural solution of the hierarchy problem. As in any theory incorporating the Equivalence Principle, the classical tests in weak gravitational fields are fulfilled as in general relativity. On the other hand, our picture suggests that Einstein general relativity may represent the weak field approximation of a theory generated from flat space with a sequence of conformal transformations. This explains naturally the absence of a {\it large} cosmological constant from symmetry breaking. Finally, one also predicts new phenomena that have no counterpart in Einstein theory such as typical `fifth force' deviations below the centimeter scale or further modifications at distances $10^{17}$ cm in connection with the Pioneer anomaly and the mass discrepancy in galactic systems.