According to the inflationary scenario of cosmology, all structure in the Universe can be traced back to primordial fluctuations during an accelerated (inflationary) phase of the very early Universe. A conceptual problem arises due to the fact that the primordial fluctuations are quantum, while the standard scenario of structure formation deals with classical fluctuations. In this essay we present a concise summary of the physics describing the quantum-to-classical transition. We first discuss the observational indistinguishability between classical and quantum correlation functions in the closed system approach (pragmatic view). We then present the open system approach with environment-induced decoherence. We finally discuss the question of the fluctuations' entropy for which, in principle, the concrete mechanism leading to decoherence possesses observational relevance.
According to the inflationary scenario of cosmology, all structure in the Universe can be traced back to primordial fluctuations during an accelerated (inflationary) phase of the very early Universe. A conceptual problem arises due to the fact that the primordial fluctuations are quantum, while the standard scenario of structure formation deals with classical fluctuations. In this essay we present a concise summary of the physics describing the quantum-to-classical transition. We first discuss the observational indistinguishability between classical and quantum correlation functions in the closed system approach (pragmatic view). We then present the open system approach with environment-induced decoherence. We finally discuss the question of the fluctuations' entropy for which, in principle, the concrete mechanism leading to decoherence possesses observational relevance.
Inflation is the standard scenario for the Early Universe providing
a mechanism to explain the generation of primordial density perturbations
from which all the structures we see in the universe formed by subsequent
gravitational growth (like, e.g., anisotropies of the Cosmic Microwave
Background, or the large-scale distribution of galaxies). The inflationary
seeds for structure formation are traced back to quantum fluctuations
of one or more (scalar) fields. However galaxies or cluster of galaxies
do behave as classical objects. This entails the issue of understanding
a quantum-to-classical transition in a cosmological framework. From
this point of view inflation and cosmological observations can represent
an interesting laboratory to explore some issues related to the quantum
measurement problem. This issue has been long known, still it has
been not explored in full details, and recently there has been a renowned
interest in it. The thesis will consist in a first part of review
of the most recent studies on the subject. It will then focus on some
aspects of the problem, namely how the classical to quantum transition
impacts on primordial gravitational waves which are a smoking gun
of inflation, and whether and how such a transition can leave specific
signatures in cosmological observables that go beyond the usual analyses
(such as, e.g., non-Gaussianity of the cosmological perturbations
from inflation).
In a previous work we have exhibited a clear description of the quantum-to-classical transition of cosmological quantum fluctuations in the inflationary scenario using the de Broglie--Bohm quantum theory. These fluctuations are believed to seed the small inhomogeneities, which are then responsible for the formation of large scale structures. In this work we show that using the de Broglie--Bohm theory, it is also possible to describe the quantum-to-classical transition of primordial perturbations which takes place around a bouncing phase, even if the latter is caused by quantum effects due to the quantization of the background geometry.
The inflationary paradigm provides a mechanism to generate the primordial perturbations needed to explain the observed large-scale structures in the Universe. Inflation traces back all the inhomogeneities to quantum fluctuations although the structures look classical today. The squeezing of primordial quantum fluctuations along with the mechanism of decoherence accounts for many aspects of this quantum-to-classical transition, although it remains a matter of debate as to whether this is sufficient to explain the issue of the realization of a single outcome (i.e. the issue of macro-objectification) from a quantum ensemble given that the Universe is a closed system. A similar question of the emergence of classical behavior of macroscopic objects exists also for laboratory systems and apart from decoherence there have been attempts to resolve this issue through continuous spontaneous localization (CSL), which is a stochastic nonlinear modification of the nonrelativistic Schr\"odinger equation. Recently, Martin et al. have investigated whether a CSL-like mechanism with a constant strength parameter---when the Mukhanov-Sasaki variable is taken as the ``collapse operator''---can explain how the primordial quantum perturbations generated during inflation become classical. Within the scope of their assumptions they essentially come to a negative conclusion. In the present work, we generalize their analysis by allowing the CSL strength parameter to depend on physical scales so as to capture the CSL amplification mechanism. We show that such a generalization provides a mechanism for the macro-objectification (i.e. classicalization) of the inflationary quantum perturbations, while also preserving the scale invariance of the power spectrum and the phase coherence of superhorizon perturbation modes in a particular class of these models.
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.
There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation. The issue is the transition from the quantum uncertainties in the homogeneous and isotropic initial state, into the late-time "classical" anisotropies and inhomogeneities. There seems to be a widespread belief that decoherence addresses the issue in a satisfactory way. This view is taken, often implicitly, by most researchers working in the field. This can be seen most clearly in those accounts intended on facing the issue directly. For instance, a recent article [C. Kiefer and D. Polarski, arXiv: 0810.0087] argues just that, and presents a detailed explanation of the justifications. The explicit nature of that account will allow us to discuss the issue in detail. There are, of course, various other works that often indirectly address the issue with similar approaches (see Refs. 2–13). This type of arguments do not only implicitly assume that decoherence offers a satisfactory solution to the measurement problem in quantum mechanics, but also that, in particular, such approach is applicable to these quantum aspects of cosmology. We will review here, why do we, together with various other researchers in the field, consider that this assumption is not correct in general. Moreover as previously discussed in Refs. 22–26, we will argue that the cosmological situation is one where the measurement problem of quantum mechanics appears in a particular exacerbated form, and that, it is this, even sharper conundrum, that should be addressed when dealing with the inflationary account of the origin of the seeds of cosmic structure in the early Universe. We briefly discuss the ideas behind what we feel might be a promising approach to deal with this problem.
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.