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arXiv:2606.21901

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

Waqas Ahmed

gr-qchep-phhep-thquant-phSubmitted Jun 20, 2026• Announced Jun 23, 2026
v1 · Jun 20, 2026v2 · Sep 21, 2026
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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 $κ(k)\propto |γ_k|^2/α_k^2$. 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

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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 κ(k)∝∣γk∣2/αk2κ(k)\propto |γ_k|^2/α_k^2κ(k)∝∣γk​∣2/αk2​. 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.
Scalar-induced gravitational waves are usually treated as a classical stochastic background sourced by phase-random curvature perturbations. We show that this description can miss residual quantum information. Starting from a decohered two-mode Gaussian scalar state, we derive explicit transfer relations between the scalar anomalous coherence and the covariance matrix of induced tensor modes. For a localized scalar power spectrum, the ordinary tensor power is sourced by scalar power contractions, whereas the opposite-mode tensor coherence is sourced by scalar anomalous-coherence contractions. This coherence can generate nonzero tensor discord and a connected tensor-power covariance even after scalar entanglement has vanished. We identify the connected covariance and phase-sensitive strain correlations as probes of primordial quantum coherence in secondary gravitational-wave backgrounds, and discuss their possible relevance for future space-based interferometers and pulsar timing arrays.
Primordial black holes (PBHs) form when large primordial curvature perturbations re-enter the Hubble radius and exceed the classical collapse threshold. These perturbations originate as quantum fluctuations of the inflationary vacuum, motivating a quantum-information description of the PBH-producing scalar sector. We develop a conservative extension of the standard PBH and scalar-induced gravitational-wave (SIGW) framework in which Gaussian quantum discord is used as a diagnostic of residual quantum correlations, not as a new PBH-formation criterion. We describe each (k,−k)(\bm k,-\bm k)(k,−k) pair as a two-mode Gaussian state and show that, in the pure squeezed limit, discord grows rapidly with the squeezing parameter, so low discord thresholds are automatically satisfied for strongly squeezed modes. The nontrivial regime is the mixed state produced by decoherence. Using a Lindblad open-system description, we motivate a Gaussian loss channel for the scalar covariance matrix and distinguish the discord from a covariance-survival factor Qdec(k)Q_{\rm dec}(k)Qdec​(k). If the decoherence channel suppresses the scalar two-point covariance, PBH abundance can be affected through the classical collapse variance, while the SIGW spectrum is modified more directly by the factors Qdec(ku)Qdec(kv)Q_{\rm dec}(ku)Q_{\rm dec}(kv)Qdec​(ku)Qdec​(kv) inside the radiation-era convolution. For a narrow scalar peak and slowly varying QdecQ_{\rm dec}Qdec​, this gives the benchmark scaling ΩGWeff≃Qdec2ΩGWclassΩ_{\rm GW}^{\rm eff}\simeq Q_{\rm dec}^2Ω_{\rm GW}^{\rm class}ΩGWeff​≃Qdec2​ΩGWclass​. Thus quantum discord and decoherence provide a controlled way to characterize the quantum-to-classical transition of PBH-producing perturbations, with the clearest imprint appearing in scalar-induced gravitational waves.
We formulate the gravitationally induced quantum decoherence of a massive object prepared in a spatial superposition. Starting from linearized gravity coupled to a massive system particle and an environmental scalar field, we derive a closed-time-path influence functional governing the reduced system dynamics. In the nonrelativistic and quasi-static regime, the decoherence exponent can be written as a bilinear functional of the difference of the system stress-energy tensors and an effective noise kernel obtained by dressing the environmental stress-energy tensor correlator with graviton propagators. We then apply this framework to the Newtonian long-range gravitational interaction and evaluate the resulting decoherence function for a dilute nonrelativistic gas modeled by finite wave packets and coarse-grained in time and space. By performing controlled approximations, we obtain analytic expressions for the cumulative decoherence function and show that the dominant contribution is accumulated logarithmically over a broad range of distances, while remaining subdominant to conventional collisional decoherence under realistic conditions.
It has been shown that the primordial perturbations sourced by inflation are driven to classicality by unitary evolution alone. However, their coupling with the environment such as photons and subsequent decoherence renders the cosmological correlations quantum, losing primordial information in the process. We argue that the quantumness of the resulting cosmological correlations is given by quantum discord, which captures nonclassical behavior beyond quantum entanglement. By considering the environment as a quantum channel in which primordial information contained in the perturbations is transmitted to us, we can then ask how much of this information is inaccessible. We show that this amount of information is given by the discord of the joint primordial perturbations-environment system. To illustrate these points, we model the joint system as a mixed bimodal Gaussian state, and show that quantum discord is dependent on the basis which decoherence occurs.
We investigate the quantumness of primordial cosmological fluctuations and its detectability. The quantum discord of inflationary perturbations is calculated for an arbitrary splitting of the system, and shown to be very large on super-Hubble scales. This entails the presence of large quantum correlations, due to the entangled production of particles with opposite momentums during inflation. To determine how this is reflected at the observational level, we study whether quantum correlators can be reproduced by a nondiscordant state, i.e. a state with vanishing discord that contains classical correlations only. We demonstrate that this can be done for the power spectrum, the price to pay being twofold: first, large errors in other two-point correlation functions that cannot however be detected since they are hidden in the decaying mode; second, the presence of intrinsic non-Gaussianity, the detectability of which remains to be determined but which could possibly rule out a nondiscordant description of the cosmic microwave background. If one abandons the idea that perturbations should be modeled by quantum mechanics and wants to use a classical stochastic formalism instead, we show that any two-point correlators on super-Hubble scales can be exactly reproduced regardless of the squeezing of the system. The latter becomes important only for higher order correlation functions that can be accurately reproduced only in the strong squeezing regime.
We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner−-−Sharp quasilocal mass and the Wald Noether−-−charge entropy in scalar−-−tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters. Within this framework, we derive explicit Einstein-frame scalar potentials: for Barrow entropy, a steep exponential potential; for Tsallis−-−Cirto entropy, an exponential potential governed by the nonextensivity parameter; and for quantum-gravity and entanglement−-−induced corrections, an approximately linear potential. These distinct potentials generate characteristic cosmological phenomenology, with implications for inflationary dynamics, late-time dark-energy behavior, and non-singular bouncing cosmologies. The framework is compatible with current constraints from solar-system tests, big-bang nucleosynthesis, and pulsar-timing observations, and it yields predictions that can be probed by forthcoming observational surveys. In this way, the analysis establishes a unified and geometrically grounded connection between information−-−theoretic entropy proposals and gravitational field theory.