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 $\Delta {\kappa }_{\mathrm{coh}}={\kappa }_N[G_{\mathrm{coh}}^{>}]-{\kappa }_N[G_{\mathrm{ref}}^{>}]$. 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 ${\kappa }_N^{\mathrm{G}}\propto e^{-4D_k}$. This provides a framework in which the SIGW spectrum fixes the signal band, while higher-order statistics probe residual coherence beyond the power spectrum.

21 pages and 7 figures