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arXiv:0905.1244 · Physica Scripta

A tomographic description for classical and quantum cosmological perturbations

Salvatore Capozzıello, Vladimir I. Man’ko, G Marmo, C Stornaiolo

Published Sep 15, 2009• 12 citations
arXivHTMLPDF

Abstract

Classical and quantum perturbations can be described in terms of marginal distribution functions in the framework of tomographic cosmology. In particular, the so-called Radon transformation and the mode-parametric quantum oscillator description can give rise to links between quantum and classical regimes. The approach results in a natural scheme to discuss the transition from quantum to classical perturbations and then it could be a workable scheme to connect primordial fluctuations with the large-scale structure observed today.

DOI
10.1088/0031-8949/80/04/045901

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Classical and quantum perturbations can be described in terms of marginal distribution functions in the framework of tomographic cosmology. In particular, the so-called Radon transformation and the mode-parametric quantum oscillator description can give rise to links between quantum and classical regimes. The approach results in a natural scheme to discuss the transition from quantum to classical perturbations and then it could be a workable scheme to connect primordial fluctuations with the large-scale structure observed today.
There is a widespread belief that the classical small inhomogeneities which gave rise to all structures in the Universe through gravitational instability originated from primordial quantum cosmological fluctuations. However, this transition from quantum to classical fluctuations is plagued with important conceptual issues, most of them related to the application of standard quantum theory to the Universe as a whole. In this paper, we show how these issues can easily be overcome in the framework of the de Broglie--Bohm quantum theory. This theory is an alternative to standard quantum theory that provides an objective description of physical reality, where rather ambiguous notions of measurement or observer play no fundamental role, and which can hence be applied to the Universe as a whole. In addition, it allows for a simple and unambiguous characterization of the classical limit.
The importance of the tomographic approach is that either in quantum mechanics as in classical mechanics the state of a physical system is expressed with marginal probability functions called tomograms. The extension of this procedure to quantum cosmology is straightforward. But in this paper, instead of using the tomographic representation, we use tomograms to analyze the properties of the quantum and classical universes, starting from the wave functions in quantum cosmology and from the phase space distributions in classical cosmology. In this, there is a part where we resume the properties of the tomograms. Then, we apply them to study and discuss the properties of the initial conditions introduced by Hartle and Hawking, Vilenkin and Linde and finally we argue about their classical transition. According to the results of this paper it follows that the decay of the cosmological constant from the Planck scale to the present one could be responsible for the transition of the quantum universe to the classical one.
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.
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).
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.
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.