We propose that the universe contains two identical sets of particles and gauge interactions, coupling only through gravitation, which differ by their Higgs potentials. We postulate that because of underlying symmetries, the two sectors when uncoupled have Higgs potentials that lie at the boundary between phases with nonzero and zero Higgs vacuum expectation. Turning on the coupling between the two sectors can break the degeneracy, pushing the Higgs potential in one sector into the domain of nonzero Higgs expectation (giving the visible sector), and pushing the Higgs potential in the other sector into the domain of zero Higgs expectation (giving the dark sector). The least massive baryon in the dark sector will then be a candidate self-interacting dark matter particle.

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