Newtonian gravity from Higgs condensates

Abstract

We propose a description of {\it Newtonian} gravity as a long wavelength excitation of the scalar condensate inducing electroweak symmetry breaking. Indeed, one finds a $-{{G_F}\over{\eta}}{{m_im_j}\over{r}}$ long-range potential where $G_F$ is the Fermi constant and $\eta\equiv {{M^2_h}\over{2m^2}} $ is determined by the ratio between the Higgs mass $M_h$ and the mass m of the elementary quanta of the symmetric phase (`phions'). The parameter $\eta$ would diverge in a true continuum theory so that its magnitude represents a measure of non-locality of the underlying field theory. By identifying $G\equiv {{G_F}\over{\eta}}$ with the Newton constant and assuming the range of Higgs mass $M_h \sim 10^{2}-10^{3}$ GeV one obtains $m=10^{-4}-10^{-5}$ eV and predicts typical `fifth-force' deviations below the centimeter scale. Relation to Einstein gravity and string theory is discussed. The crucial role of the first-order nature of the phase transition for the solution of the so-called `hierarchy problem' is emphasized. The possible relevance of the picture for the self-similarity of the universe and for a new approach to the problem of dark matter is discussed.