Abstract:We propose a quantum bosonic qubit model on a fcc lattice that realizes the canonical source structure of mimetic dark matter as a defect of a rank-two lattice Gauss law. The standard contribution from general relativity is implemented similarly to previous work in the literature, while the mimetic sector modifies the constraint equations through additional source terms. Different theories such as mimetic dark matter, vector mimetic dark matter, and tensor-vector-scalar models are implemented on the lattice. In all these cases, a generalized Gauss law incorporates an additional Gauss-law (topological) defect depending on the type of generalization, but always fitting into the structure of the defects from the general relativity contribution. We also derive the resulting charge-selection rules for the defect sectors and show, in a worked example, that a localized defect sources a long-range rank-two field whose trace-free representative is exactly the Bowen-York momentum solution of canonical gravity. The mimetic constraint is treated in its full ADM form, retaining the normal derivative of the scalar field, and the known ghost and gradient instabilities of the minimal continuum mimetic theory are summarized. The lattice construction is therefore presented as a formal realization of the canonical source structure rather than as a complete cosmological model.
From: Luis Lozano [view email]
[v1]
Tue, 24 Dec 2019 06:42:22 UTC (100 KB)
[v2]
Tue, 31 Dec 2019 17:24:26 UTC (101 KB)
[v3]
Wed, 10 Jun 2026 05:57:52 UTC (110 KB)
[v4]
Mon, 20 Jul 2026 18:15:44 UTC (119 KB)
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