Entanglement, Discord, and Residual Coherence in Scalar-Induced Gravitational Waves

Abstract:Scalar-induced gravitational waves (SIGWs) are usually characterized by their power spectrum, although their quadratic scalar source also carries higher-order correlation information. We investigate whether phase-sensitive correlations of a primordial Gaussian scalar state can survive decoherence and be transferred to the induced tensor sector. The scalar state is described in a fixed oscillator basis by the occupation $N_k^\zeta$ and anomalous moment $M_k^\zeta$, while the transfer is formulated through the unequal-time scalar Wightman function. The late-time tensor moments $d_k$ and $\gamma_k$ define an effective Gaussian reference state and its discord, whereas the exact SIGW state is generally non-Gaussian and contains an additional connected fourth-order cumulant. We therefore introduce the baseline-subtracted observable $\Delta\kappa_{\rm coh}=\kappa_N[G^>_{\rm coh}]-\kappa_N[G^>_{\rm ref}]$. For phase damping with $M_k^\zeta\propto e^{-D_k}$, the Gaussian-reference contribution conditionally scales as $|\gamma_k|\propto e^{-2D_k}$ and $\kappa_N^{\rm G}\propto e^{-4D_k}$. This provides a framework in which the SIGW spectrum fixes the signal band, while higher-order statistics probe residual coherence beyond the power spectrum.

arXiv:2606.21901 [gr-qc]

(or arXiv:2606.21901v2 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2606.21901 Focus to learn more arXiv-issued DOI via DataCite

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