Quantum entanglement in TAUB supersymmetric cosmologies: a microsuperspace analysis

We study the entanglement entropy in the context of supersymmetric quantum cosmology, focusing on a pair of TAUB-type universes within the microsuperspace sector \((R_{2}\rightarrow 0)\). Starting from the Lagrangian of a supergravity theory with \(\mathcal {N}=1\) in \(D=4\), we construct the quantum Hamiltonian and obtain solutions to the Wheeler-DeWitt equation restricted to the subspace defined by first-order fermionic constraints. The resulting solutions take the form of four-component spinor-like wavefunctions, allowing a natural interpretation in terms of internal degrees of freedom. This spinorial structure enables the construction of an entangled state between two identical wavefunctions, formulated as a bilinear combination of the spin states, analogous to the bipartite entanglement of two electrons. We then compute the entanglement entropy between two such universes, each described by spinorial wavefunctions. The analysis reveals that the entropy is maximized for specific combinations of the Misner variables \(\Omega _{i}\) and \(\beta _{\pm i}\), with \(i=I,II\) labeling each universe. We interpret these maxima as configurations of maximal quantum correlation determined by the geometric size and anisotropy of the universes. The role of anisotropy in modulating the entanglement is also elucidated.