Expanding Our Horizons: Rethinking Gravity's Role in the Quantum-to-Classical Transition

This paper investigates whether gravitational dynamics during inflation are sufficient to drive the quantum-to-classical transition of primordial fluctuations. It challenges the standard assumption that super-horizon dynamics and decoherence inevitably render cosmic structure classical, suggesting instead that quantum signatures may persist in observable structures through non-linear interactions.

The limitations of traditional lore

Standard cosmological models often rely on decoherence without decoherence, where super-horizon dynamics drive quantum states into a highly-squeezed configuration. In this state, the commutator between the field and its conjugate momentum becomes negligible compared to classical correlations, making the system appear classical. However, the author argues that this argument is limited because it applies primarily to the linear level of the free theory where states remain Gaussian.

The paper highlights several specific limitations to using squeezing as a proxy for classicality:

• Squeezing is not an intrinsic measure of classicality and can be altered via canonical transformation.

• The same super-horizon dynamics behind squeezing are also responsible for producing strong entanglement between Fourier modes, keeping the CMB in a very quantum state.

• Interactions beyond the linear order generate non-Gaussianities that produce interference patterns in phase space which cannot be squeezed away.

Wigner negativity as a diagnostic

To move beyond the ambiguities of squeezing, the paper proposes using the Wigner function W(x, p) as a sharper diagnostic of classicality. Because Hudson’s theorem states that the only pure state with a globally positive Wigner function is a single Gaussian, any non-linear evolution will generically introduce negativity somewhere in phase space. This negativity serves as an indicator of genuine quantum coherences and interference between different branches of the wavefunction.

The central question is whether gravitational dynamics inevitably suppress this Wigner negativity or if it can persist in a way that leaves imprints on cosmological observables. If the relevant observables do not have support where the Wigner function is negative, the system will appear classical; however, non-linearities may prevent this suppression.

Non-attractor dynamics and growing negativity

The paper demonstrates that in non-attractor backgrounds, such as constant-roll or ultra-slow roll inflation, quantum effects can actually grow on super-horizon scales. In these settings, the inflaton’s velocity is not uniquely determined by its position, causing curvature perturbations to continue evolving rather than freezing. This leads to several critical consequences:

• The effective couplings of perturbations inherit time dependence from the background evolution.

• Non-linear evolution produces oscillations, and regions of negativity in the Wigner function, appearing as interference fringes.

• In ultra-slow roll backgrounds, the negativity volume N grows exponentially with the number of e-folds.

Decoherence and observational prospects

While the cosmological horizon provides a natural system-environment split that should lead to decoherence, it is unclear if this process is efficient enough to erase quantum features. The paper identifies three major caveats regarding standard decoherence estimates:

1. Diagnostic-dependence: Traditional measures like purity or entanglement entropy do not map directly onto observables as effectively as the Wigner function.

2. Gravity is weak: Gravitational self-interactions are inherently weak, meaning decoherence mediated by gravity may be slow and inefficient.

3. Non-attractor backgrounds: Enhanced interactions in these phases may generate negativity faster than decoherence can suppress it.

Ultimately, the paper suggests that if oscillatory features are confined to the tails of the distribution, their consequences might be found in rare events rather than standard lower-point statistics.

1. Wigner-Negativity Diagnostic for Quantum Machine Learning (QML) Validation

• Improvement: Integrate a phase-space monitoring layer into QML training loops that utilizes the Wigner-Weyl transform to calculate the negativity volume (N) of the quantum state, rather than relying on traditional purity or entanglement entropy metrics.

• Capability: The AI system can distinguish between pseudo-classical states (highly squeezed states that appear classical but are actually just highly correlated) and genuinely quantum states (states exhibiting Wigner negativity). This prevents the AI from wasting computational resources on quantum circuits that have effectively decohered into classical stochastic samplers, ensuring the hardware is actually leveraging non-classical interference for speedup.

2. Non-Attractor Latent Dynamics for Generative Diffusion Models

• Improvement: Replace standard Gaussian noise/Ornstein-Uhlenbeck processes in the reverse diffusion step with non-attractor dynamics, where the latent variable evolution is governed by time-dependent effective couplings that allow for the growth of non-linearities and non-Gaussianity on super-horizon (large scale) latent trajectories.

• Capability: The AI can generate high-fidelity synthetic data that captures complex, multi-scale interference patterns and high-order non-linear correlations (e.g., in fluid turbulence or complex biological textures) which are typically smoothed out by standard Gaussian diffusion models that assume a slow-roll or attractor-based approach to noise reduction.

3. Horizon-Based System-Environment Robustness Framework

• Improvement: Implement a Cosmological Horizon testing architecture for Reinforcement Learning (RL) agents, where the environment is explicitly partitioned into an observable system and an unobserved, high-frequency environment. The interaction is modeled using non-linear gravitational-style self-interactions that couple the agent's actions to these unobserved modes.

• Capability: The AI system can undergo much more rigorous stress testing against structured decoherence. Instead of merely being robust to additive white noise, the agent becomes capable of maintaining stable decision-making in complex, non-linear environments where noise is actually an entangled, unobservable component of the system's own dynamics.

4. Phase-Space Tail-Event Anomaly Detection

• Improvement: Develop an anomaly detection engine that uses Wigner function analysis to identify interference fringes in the phase-space distribution of high-dimensional sensor data, specifically looking for signatures in the tails of the distribution rather than the mean or variance.

• Capability: The system can detect extremely subtle, non-linear precursors to system failures (e.g., in high-frequency trading or aerospace telemetry) that appear perfectly normal when viewed through standard first and second-order statistics (like power spectra or mean squared error) but exhibit non-classical oscillatory patterns in their phase-space representation.

The origin of cosmic structure is widely regarded as quantum, yet the Universe today appears classical. Standard lore attributes this to a "quantum-to-classical" transition on super-horizon scales during inflation. Gravity plays a central role: super-horizon dynamics squeeze quantum states, while the cosmological horizon enforces a system-environment split, leading to decoherence. But are these mechanisms always sufficient? We revisit this question, identifying assumptions and limitations in conventional arguments. We highlight recent work showing that beyond slow roll, non-linear dynamics of cosmological perturbations can generate and amplify quantum coherence at the closed-system level. Preliminary results further suggest that, for the minimal irreducible contribution to decoherence coming from stochastic kicks at the coarse-graining scale, the rate of coherence generation can outpace the decoherence rate. This raises the possibility that signatures of a quantum origin may persist in cosmic structure. We propose a phase-space analysis based on the Wigner function as a concrete route to identifying and probing such signatures.