  We 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 $M \gg M_{\rm Pl}$ 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 $SO(3,1)_{space}\times SO(3,1)_{spin}$ 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 $G_N$.

General Relativity and Quantum Cosmology;Astrophysics;Other Condensed Matter;High Energy Physics - Phenomenology