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Emergent Electroweak Gravityby: Bob McElrath
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AbstractWe show that any massive cosmological relic particle with small self-interactions is a super-fluid today, due to the broadening of its wave packet, and lack of any elastic scattering. The WIMP dark matter picture is only consistent its mass $M \gg M_ Pl$ in order to maintain classicality. The dynamics of a super-fluid are given by the excitation spectrum of bound state quasi-particles, rather than the center of mass motion of constituent particles. If this relic is a fermion with a repulsive interaction mediated by a heavy boson, such as neutrinos interacting via the $Z^0$, the condensate has the same quantum numbers as the vierbein of General Relativity. Because there exists an enhanced global symmetry $SO(3,1)_space× SO(3,1)_spin$ among the fermion's self-interactions broken only by its kinetic term, the long wavelength fluctuation around this condensate is a Goldstone graviton. A gravitational theory exists in the low energy limit of the Standard Model's Electroweak sector below the weak scale, with a strength that is parametrically similar to $G_N$.
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