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

Abstract

Scalar-induced gravitational waves are usually modeled as a classical stochastic background sourced by primordial curvature perturbations. We investigate whether residual quantum-information properties of the scalar sector can survive decoherence and leave imprints in the induced tensor background. Using the covariance-matrix formalism, we describe primordial curvature perturbations as decohered two-mode squeezed Gaussian states and identify the anomalous scalar coherence that may remain after scalar entanglement has vanished. We then derive the leading scalar-to-tensor transfer relations for opposite-momentum induced tensor modes. The ordinary tensor power is sourced by scalar power contractions, whereas the opposite-mode tensor coherence is sourced by anomalous scalar-coherence contractions. This tensor coherence controls the induced Gaussian discord and generates connected and phase-sensitive observables, including a connected power covariance $\kappa (k)\propto |{\gamma }_k{|}^2/{\alpha }_k^2$. Thus the robust signature is not a universal shift of the gravitational-wave spectrum, but a correlated tensor background with nontrivial covariance and phase structure. We discuss phenomenological templates and provide an illustrative Fisher estimate for future gravitational-wave observations. Our results suggest that scalar-induced gravitational waves may offer a new probe of primordial quantum correlations beyond entanglement.

Comments: 30 pages and 7 figures