Emergent Dark Matter and Dark Energy from a Lattice Model

We propose a quantum bosonic qubit model on a fcc lattice to obtain mimetic dark matter. The general relativity contribution is implemented similarly to other works but it differs strongly on the implementation of the constraint equations and their meaning. Different theories as mimetic dark matter, the vector mimetic dark mater, and tensor-vector-scalar models are implemented on the lattice. In all these cases, a generalized Gauss' law incorporates an additional topological defect depending on the type of generalization, but always fitting in the structure of the topological defects from general relativity contribution.