Was the Early Universe Quantum? Falsifying Classical Stochastic Inflation

TL;DR

The paper interrogates whether primordial fluctuations require a quantum description or could arise from a classical stochastic process. It formulates a falsification-based framework by defining a precise classical hypothesis with a positive probability distribution and deriving inequality constraints on higher-order statistics that must hold under $H_{ m C}$ but can be violated by quantum states, notably through conditional-variance bounds. The authors show that decoherence typically erases quantum coherence, but symmetry-protected spectator sectors can prolong coherence (with decoherence rate $\Gamma_{\rm dec} \sim g^2 H$, $g\ll1$), enabling observable violations of the classicality inequalities. They map the test to observational pathways using large-scale structure and 21 cm surveys, introducing the deficit parameter $\mathcal{E}=1-r^2$ and linking its resolvability to the effective number of modes $N_m^{\rm eff}$, with forecasts suggesting percent-level sensitivities for multi-tracer surveys and sub-percent sensitivities for next-generation 21 cm experiments. Ultimately, the work reframes primordial quantumness as a data-driven falsification of classical stochastic inflation, offering a concrete, realizable route to empirically test the quantum origin of cosmological perturbations.

Abstract

Inflationary cosmology successfully accounts for the observed properties of primordial fluctuations using quantum field theory in an expanding background. However, the quantum nature of these fluctuations has not been experimentally established, since classical stochastic models could reproduce the observed two-point statistics by construction. Existing approaches to testing primordial quantumness focus primarily on Bell inequalities, which provide a sharp conceptual criterion but are difficult to implement with cosmological observables. In this work we adopt a falsification-based approach. We define a precise classical hypothesis for the origin of primordial perturbations (local stochastic fields admitting a positive probability distribution) and identify inequality constraints that must be satisfied within this class. We show how violations of these classicality inequalities can be probed using realistic cosmological observables, without invoking Bell tests or non-commuting measurement settings. We further identify symmetry-protected spectator sectors in which quantum coherence is parametrically preserved during inflation, allowing violations of observable magnitude to survive decoherence. Our results show that large-scale structure and future 21 cm surveys provide a viable and quantitative route to falsifying classical stochastic descriptions of primordial fluctuations.

Figures (1)

• Figure 1: Minimum resolvable deficit $\Delta\mathcal{E}$ of the conditional-variance statistic $\mathcal{E}=1-r^2$ as a function of the effective number of usable Fourier modes $N_m^{\rm eff}$. The solid curve shows the Gaussian scaling $\Delta\mathcal{E}_{\min}\simeq 2/\sqrt{N_m^{\rm eff}}$, while the dashed curve illustrates the impact of foregrounds and systematics, modeled as a reduction $N_m^{\rm eff}=0.3\,N_m$. The horizontal dotted line indicates an illustrative classical bound for local stochastic models with bounded noise $\mathcal{E}^{(\mathrm{cl})}=10^{-2}$, while the shaded horizontal band highlights the range $\Delta\mathcal{E}\sim10^{-3}$–$10^{-2}$ naturally populated by symmetry-protected spectator sectors, for which decoherence is parametrically suppressed ($\Gamma_{\rm dec}\sim g^2H\ll H$). Shaded vertical bands indicate representative ranges of $N_m^{\rm eff}$ for multi-tracer galaxy surveys (DESI, Euclid, Roman), post-reionization 21 cm intensity mapping experiments (HIRAX- and PUMA-like), and an idealized dark-ages 21 cm survey. Crossing the classical bound corresponds to falsification of a classical stochastic description of primordial fluctuations.