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arXiv:1309.2670 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum-to-classical transition of primordial cosmological perturbations in de Broglie-Bohm quantum theory: The bouncing scenario

Nelson Pinto-Neto, Grasiele Batista dos Santos, Ward Struyve

Published Jan 14, 2014• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevd.89.023517

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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.
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.
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).
The quantum cosmology of the flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe, filled with a scalar field, is considered in the de Broglie--Bohm (dBB) interpretation framework. A stiff-matter quantum bounce solution is obtained. The bouncing and subsequent pre-inflationary and inflationary dynamics are studied in details. We consider some representative primordial inflation models as examples, for which analytical expressions characterizing the dynamical quantities can be explicitly derived. The dependence of the inflationary dynamics on the quantum bounce parameters is then analyzed. The parameters emerging from our description are constrained by requiring the produced dynamics to be in accordance with some key cosmological quantities. The constraining conditions are also illustrated through regions of parameter space in terms of the bounce quantities.
We review the main results that have been obtained in quantum cosmology from the perspective of the de Broglie-Bohm quantum theory. As it is a dynamical theory of assumed objectively real trajectories in the configuration space of the physical system under investigation, this quantum theory is not essentially probabilistic and dispenses the collapse postulate, turning it suitable to be applied to cosmology. In the framework of minisuperspace models, we show how quantum cosmological effects in the de-Broglie-Bohm's approach can avoid the initial singularity, and isotropize the Universe. We then extend minisuperspace in order to include linear cosmological perturbations. We present the main equations which govern the dynamics of quantum cosmological perturbations evolving in non-singular quantum cosmological backgrounds, and calculate some of their observational consequences. These results are not known how to be obtained in other approaches to quantum theory. In the general case of full superspace, we enumerate the possible structures of quantum space and time that emerge from the de Broglie-Bohm picture. Finally, we compare some of the results coming from the de Broglie-Bohm theory with other approaches, and discuss the physical reasons for some discrepancies that occur.
We review the de Broglie–Bohm quantum theory. It is an alternative description of quantum phenomena in accordance with all the quantum experiments already performed. Essentially, it is a dynamical theory about objectively real trajectories in the configuration space of the physical system under investigation. Hence, it is not necessarily probabilistic, and it dispenses with the collapse postulate, making it suitable to be applied to cosmology. The emerging cosmological models are usually free of singularities, with a bounce connecting a contracting era with an expanding phase, which we are now observing. A theory of cosmological perturbations can also be constructed under this framework, which can be successfully confronted with current observations, and can complement inflation or even be an alternative to it.