Bipartite entanglement of the primordial Majorana during inflation

• URL: http://arxiv.org/abs/2606.26869v1
• Date: Thu, 25 Jun 2026 10:55:03 GMT
• Title: Bipartite entanglement of the primordial Majorana during inflation
• Abstract summary: We use a primordial Majorana field as a fermionic probe of quantum correlations during inflation.<n>We compute the von Neumann entropy of the reduced mode and the logarithmic negativity of the Majorana pair.
• Score: 0.18352113484137625
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We use a primordial Majorana field as a fermionic probe of quantum correlations during inflation. Working in a torsion-free FLRW spacetime, we derive the two-component Majorana mode equations in an axion-inflation background and construct the corresponding quadratic Hamiltonian in the paired momentum basis. Hamiltonian diagonalization and the fermionic squeezing formalism are shown to give the same Bogoliubov transformation, providing a direct map from the Majorana mode functions to the instantaneous occupation number and to the two-mode state of each $(\boldsymbol{k},-\boldsymbol{k})$ pair. Because Fermi statistics restricts each helicity sector to the vacuum and one-pair states, the resulting Hilbert space is finite and the bipartite quantum-information measures can be evaluated explicitly. We compute the von Neumann entropy of the reduced mode and the logarithmic negativity of the Majorana pair. Both diagnostics indicate that sufficiently light Majorana modes can retain enhanced super-horizon bipartite quantumness, with the logarithmic negativity making the residual inseparability especially explicit. Our result does not by itself constitute an observational Bell test or a complete decoherence analysis; rather, it identifies a Pauli-bounded matter sector in which horizon exit alone is not sufficient to erase the quantum signature encoded in the two-mode state, thereby motivating an open-system study of how reheating and inflaton-induced interactions classicalize primordial fermionic probes.

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