We analyze the emergence of classical cosmological spacetimes in quantum cosmology by computing the reduced density matrix for long-wavelength curvature perturbations. Starting from standard Hartle--Hawking and tunneling boundary conditions, we emphasize that semiclassical WKB structure and inflationary squeezing do not by themselves yield classicality. Tracing over unobserved degrees of freedom and using the influence functional formalism, we derive the decoherence functional for superhorizon curvature modes during inflation. For a light massive environmental scalar field in the Bunch--Davies vacuum, we obtain an explicit noise kernel and show how a nonzero mass regulates the infrared behavior. We then evaluate decoherence under horizon-based and EFT-motivated coarse grainings, finding efficient suppression of interference between macroscopically distinct perturbation histories in both cases. The analysis clarifies the distinct roles of boundary conditions (branch amplitudes) and decoherence (classical branch selection) and yields an emergent cosmological arrow of time through environment-induced entanglement.
We analyze the emergence of classical cosmological spacetimes in quantum cosmology by computing the reduced density matrix for long-wavelength curvature perturbations. Starting from standard Hartle--Hawking and tunneling boundary conditions, we emphasize that semiclassical WKB structure and inflationary squeezing do not by themselves yield classicality. Tracing over unobserved degrees of freedom and using the influence functional formalism, we derive the decoherence functional for superhorizon curvature modes during inflation. For a light massive environmental scalar field in the Bunch--Davies vacuum, we obtain an explicit noise kernel and show how a nonzero mass regulates the infrared behavior. We then evaluate decoherence under horizon-based and EFT-motivated coarse grainings, finding efficient suppression of interference between macroscopically distinct perturbation histories in both cases. The analysis clarifies the distinct roles of boundary conditions (branch amplitudes) and decoherence (classical branch selection) and yields an emergent cosmological arrow of time through environment-induced entanglement.
After a brief summary of the four main veins in the treatment of decoherence and quantum to classical transition in cosmology since the 1980s, we focus on one of these veins in the study of quantum decoherence of cosmological perturbations in inflationary universe, the case when it does not rely on any environment. This is what ‘intrinsic’ in the title refers to—a closed quantum system, consisting of a quantum field which drives inflation. The question is whether its quantum perturbations, which interact with the density contrast giving rise to structures in the universe, decohere with an inflationary expansion of the universe. A dominant view which had propagated for a quarter of a century asserts yes, based on the belief that the large squeezing of a quantum state after a duration of inflation renders the system effectively classical. This paper debunks this view by identifying the technical fault-lines in its derivations and revealing the pitfalls in its arguments which drew earlier authors to this wrong conclusion. We use a few simple quantum mechanical models to expound where the fallacy originated: The highly squeezed ellipse quadrature in phase space cannot be simplified to a line, and the Wigner function cannot be replaced by a delta function. These measures amount to taking only the leading order in the relevant parameters in seeking the semiclassical limit and ignoring the subdominant contributions where quantum features reside. Doing so violates the bounds of the Wigner function, and its wave functions possess negative eigenvalues. Moreover, the Robertson-Schrödinger uncertainty relation for a pure state is violated. For inflationary cosmological perturbations, in addition to these features, entanglement exists between the created pairs. This uniquely quantum feature cannot be easily argued away. Indeed, it could be our best hope to retroduce the quantum nature of cosmological perturbations and the trace of an inflation field. All this points to the invariant fact that a closed quantum system, even when highly squeezed, evolves unitarily without loss of coherence; quantum cosmological perturbations do not decohere by themselves.
This preprint develops a model-independent diagnostic framework for evaluating decoherence efficiency in inflationary curvature perturbations within an open quantum system formulation. The work does not introduce a new decoherence mechanism; instead, it constructs a normalized dimensionless functional intended to provide a systematic basis for comparing environmental decoherence scenarios in primordial cosmology. A persistence functional is derived to characterize the attenuation of off-diagonal density matrix components under inflationary expansion. Using a representative toy open-system model, the analysis demonstrates that the functional exhibits rapid suppression behavior associated with the exponential growth of comoving volume during inflation. The framework further suggests that residual quantum coherence may contribute to higher-order correlation functions of curvature perturbations. Accordingly, observational constraints on primordial non-Gaussianity may be interpreted as indirect lower bounds on decoherence efficiency. The formulation is intended as a diagnostic tool rather than a proposal of a new physical decoherence process. Keywords : Inflationary Cosmology Quantum Decoherence Primordial Perturbations Open Quantum Systems Classicality Non-Gaussianity
The emergence of preferred classical variables within a many-body wavefunction is encoded in its entanglement structure in the form of redundant classical information shared between many spatially local subsystems. We show how such structure can be generated via cosmological dynamics from the vacuum state of a massless field, causing the wavefunction to branch into classical field configurations on large scales. An accelerating epoch first excites the vacuum into a superposition of classical fields as well as a highly sensitive bath of squeezed super-horizon modes. During a subsequent decelerating epoch, gravitational interactions allow these modes to collect information about longer-wavelength fluctuations. This information disperses spatially, creating long-range redundant correlations in the wavefunction. The resulting classical observables, preferred basis for decoherence, and system/environment decomposition emerge from the translation invariant wavefunction and Hamiltonian, rather than being fixed by hand. We discuss the role of squeezing, the cosmological horizon scale, and phase information in the wavefunction, as well as aspects of wavefunction branching for continuous variables and in field theories.
Description : This work introduces a novel, model-independent diagnostic framework for quantifying quantum decoherence in primordial inflationary perturbations. The study addresses the fundamental problem of the quantum-to-classical transition in cosmology by defining a normalized persistence functional that captures the suppression of quantum coherence over time. Within an open quantum system approach, each perturbation mode is treated as an effective quantum degree of freedom interacting with an environment, leading to Gaussian suppression of off-diagonal density matrix elements. The proposed functional provides a direct and scalable measure of decoherence efficiency without relying on detailed microscopic modeling. A key feature of the framework is the introduction of a residual coherence parameter, which accounts for possible late-time deviations from complete classicalization. The work further establishes a monotonicity property for the decoherence functional and connects the persistence measure to entropy growth, offering an information-theoretic interpretation of the decoherence process. Importantly, the framework suggests a phenomenological link between residual coherence and observable non-Gaussianity in the cosmic microwave background, opening a pathway for potential observational constraints. The proposed diagnostic functional is broadly applicable across inflationary models and provides a unified tool for comparing decoherence efficiency under different environmental interactions. This work lays the foundation for future studies on quantum signatures in cosmological observables and the persistence of quantum features in the early universe. Keywords : Quantum Decoherence Inflationary Cosmology Primordial Perturbations Open Quantum Systems Quantum-to-Classical Transition Non-Gaussianity Cosmological Perturbation Theory Density Matrix Quantum Cosmology Early Universe Physics Decoherence Functional Entropy and Information Theory
Recent results on the decoherent histories quantization of simple cosmological models (minisuperspace models) are described. The most important issue is the construction, from the wave function, of a probability distribution answering various questions of physical interest, such as the probability of the system entering a given region of configuration space at any stage in its entire history. A standard but heuristic procedure is to use the flux of (components of) the wave function in a WKB approximation as the probability. This gives sensible semiclassical results but lacks an underlying operator formalism. Here, we supply the underlying formalism by deriving probability distributions linked to the Wheeler-DeWitt equation using the decoherent histories approach to quantum theory, building on the generalized quantum mechanics formalism developed by Hartle. The key step is the construction of class operators characterizing questions of physical interest. Taking advantage of a recent decoherent histories analysis of the arrival time problem in non-relativistic quantum mechanics, we show that the appropriate class operators in quantum cosmology are readily constructed using a complex potential. The class operator for not entering a region of configuration space is given by the S-matrix for scattering off a complex potential localized in that region. We thus derive the class operators for entering one or more regions in configuration space. The class operators commute with the Hamiltonian, have a sensible classical limit and are closely related to an intersection number operator. The corresponding probabilities coincide, in a semiclassical approximation, with standard heuristic procedures.
This paper addresses a fundamental unresolved problem in inflationary cosmology: what quantum-state structure makes the one-realization classical description used in late-time cosmology physically meaningful within unitary quantum theory? We identify a structure that supports such a description, which we call Cosmological Classical Branches (CCBs). After reheating, the curvature perturbation is a collective variable rather than an independent subsystem. This shifts the classicality problem from the reduced state of the curvature perturbation itself to records of primordial information in the post-reheating matter state. When distinct matter components respond to the same primordial realization and their conditional states become distinguishable across different realizations, they carry records of the information about the curvature perturbation. A record in one component makes the realization readable, while a compatible record in a disjoint component suppresses interference accessible to operations confined to the first component, forming CCBs. Conditioning on a physical record yields a one-realization description within a CCB, in which the resolved primordial value acts as a c-number label while the matter degrees of freedom remain quantum. We test this criterion using effective models of two radiation fluids during radiation domination and of photons and cold dark matter around radiation--matter equality. We also show that a CCB typical with respect to the primordial Born measure exhibits the expected one-realization statistics: mode averages approach the primordial two-point statistics at fixed nonzero wavenumber in the large-volume limit. Overall, these results provide an operational framework at the quantum-state level connecting the primordial quantum superposition to the one-realization cosmological history assumed in standard cosmology.