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How the Primordial Sky Became Classical: Quantum Darwinism of Cosmological Perturbations

Rolando P. Hong Enriquez

Published Jul 14, 2026• 0 citations
Publisher

Abstract

Inflation stretches quantum vacuum fluctuations into the density ripples we later see imprinted on the cosmic microwave background, yet the initial state is a pure, highly squeezed quantum state. The usual explanation for why those ripples look classical appeals to decoherence and the fading of a "decaying mode." This paper argues that the sharper statement is objectivity: the ripples become a fact for all observers, in the precise sense of quantum Darwinism, exactly when the growing perturbation is redundantly recorded across a vast environment of short-wavelength and gravitational-wave modes. The paper models a single super-horizon mode and its environment exactly. It proves that, once the mode crosses the horizon, its amplitude is recorded so redundantly that even a tiny fragment of the environment already fixes it, while the number of independent records grows without bound as the universe expands. Horizon crossing is therefore a Darwinism–encoding transition: an information measure rises from zero to one bit as the mode freezes. And the environment singles out one objective observable — the curvature amplitude — while its conjugate is only globally encoded, readable by no bounded fragment. The results are closed-form, and their exact algebraic cores are verified by proof-checking software. The record strength is not a free parameter: it is fixed by the mode's decoherence, computed from gravitational theory, and the leftover quantum coherence falls off exponentially with the redundancy. In short: the sky is classical not merely because it decohered, but because horizon crossing broadcast it — copying each primordial fluctuation until it became a fact for everyone.

DOI
10.5281/zenodo.21356393

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Inflationary cosmology faces a fundamental gap between primordial quantum fluctuations and the classical cosmic history inferred from observations. Although the primordial quantum state is a superposition of field configurations, standard cosmology assumes one definite realization of curvature perturbations and uses classical perturbation theory to describe the resulting gravitational potentials, CMB anisotropies, and large-scale structure. Squeezing and decoherence of primordial fluctuations alone do not explain why this one-realization description is physically meaningful. We address this issue through Cosmological Classical Branches (CCBs), using the quantum-information-theoretic notion of physical records. In CCBs, distinct late-time matter components carry compatible records of the same primordial configuration. A record in one component makes that configuration readable, while a disjoint compatible record suppresses interference accessible to operations on the first. Each branch thus admits a common c-number primordial label at finite resolution, while the global quantum superposition persists. This Letter summarizes the framework developed in Ref.~\cite{Kuroda2026CCB}.
Quantum Darwinism describes how a classical, objective world emerges when a system's information is redundantly copied into its environment. Existing theory is largely static: it asks whether a given state already has this objective structure. This paper develops the complementary dynamical picture — how objectivity emerges and why it is stable. It builds a genuine "renormalization group," a physicist's tool for tracking how a system looks as one zooms out, and applies it to the environmental record. The central finding is that objectivity is a fixed point of this zooming-out flow: an objective state stays objective at every scale, and — strikingly — the requirement of scale-invariance forces the records to be genuinely classical. The flow has two stable end-states, an "objective" phase and a scrambled "encoded" phase, separated by a sharp transition at a critical broadcast rate. The paper proves that a natural information measure decreases irreversibly along the flow toward objectivity, giving the emergence of classicality a definite arrow, analogous to celebrated "c-theorems" in the physics of critical phenomena. A known model of the objectivity–scrambling transition is recovered as a special limit. Every quantitative claim is reproduced by self-testing code, and the core theorems are additionally verified by proof-checking software. In short: classicality has a direction. Like heat flowing one way, the world coarse-grains toward objectivity and never back — a c-theorem for the quantum-to-classical transition.
In the Bose–Marletto–Vedral (BMV) proposal, two masses placed in superposition become entangled only if the gravitational field between them is quantum — a proposed table-top test of whether gravity is quantum. This paper reframes the question through quantum Darwinism. A mass's Newtonian field is a record of its position imprinted on nearby matter; a classical field is one that broadcasts that record objectively, whereas a genuinely quantum field can remain in superposition and refuses to copy a which-path record. The paper models exactly a source in superposition, its recording environment, and its partner mass, and proves an objectivity–entanglement monogamy: if the field records the position redundantly across many fragments, the entanglement it can generate is exponentially small in that redundancy — a field cannot both broadcast and entangle. Several results follow. The field record is extensive. A sharp classical-versus-quantum dichotomy is carried by an information measure that rises from zero to one bit as the field becomes classical. The source's position is the unique objective observable. And earlier black-hole decoherence results reappear as the single-fragment limit. A measured entanglement therefore bounds the field's objective redundancy from above. The results are finite-dimensional theorems with exact numerics reproduced by self-testing code, and two algebraic cores are additionally verified by proof-checking software; the gravitational couplings and decoherence rates are imported, not re-derived. In short: a field cannot both broadcast and entangle — so the entanglement a BMV experiment measures is precisely the price gravity pays for not being classical.