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Cambridge University Press eBooks

Quantum Origin of Cosmological Structure and Dynamical Reduction Theories

Daniel Sudarsky

Published Jan 1, 2017• 1 citation
Publisher

Abstract

Introduction Contemporary cosmology includes inflation as one of its central components. It corresponds to a period of accelerated expansion thought to have occurred very early in cosmic history, which takes the universe from relatively generic post Planckian era conditions to a stage where it is well described (with exponential accuracy in the number of e-folds) by a flat Robertson–Walker space-time (which describes a homogeneous and isotropic cosmology). It was initially proposed to resolve various naturalness problems: flatness, horizons, and the excess of massive relic objects, such as topological defects, that were expected to populate the universe according to grand unified theories (GUT). Nowadays, it is lauded because it predicts that the universe's mean density should be essentially identical to the critical value, a very peculiar situation which corresponds to a spatially flat universe. The existing data support this prediction. However, its biggest success is claimed to be the natural account for the emergence of the seeds of cosmic structure in terms of primordial quantum fluctuations, and the correct estimate of the corresponding microwave spectrum. This represents, thus, a situation which requires the combined application of general relativity (GR) and quantum theory, and that, moreover, is tied with observable imprints left from the early universe, in both the radiation in cosmic microwave background (CMB), and in the large scale cosmological structure we can observe today. It should not be surprising that, when dealing with attempts to apply our theories to the universe as a whole, we should come face to face with some of the most profound conceptual problems facing our current physical ideas. In fact, J. Hartle had noted long ago [28] that serious difficulties must be faced when attempting to apply quantum theory to cosmology, although the situations that were envisioned in those early works corresponded to the even more daunting problem of full quantum cosmology, and not the limited use of quantum theory to consider perturbative aspects, which is what is required in the treatment of the inflationary origin of the seeds of cosmic structure. This led him and his collaborators to consider the Consistent Histories framework, which is claimed to offer a version of quantum theory that does not rely on any fundamental notion of measurements, as the favored approach to use in such contexts. We will have a bit more to say about this shortly.

DOI
10.1017/9781316535783.018

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Introduction Contemporary cosmology includes inflation as one of its central components. It corresponds to a period of accelerated expansion thought to have occurred very early in cosmic history, which takes the universe from relatively generic post Planckian era conditions to a stage where it is well described (with exponential accuracy in the number of e-folds) by a flat Robertson–Walker space-time (which describes a homogeneous and isotropic cosmology). It was initially proposed to resolve various naturalness problems: flatness, horizons, and the excess of massive relic objects, such as topological defects, that were expected to populate the universe according to grand unified theories (GUT). Nowadays, it is lauded because it predicts that the universe's mean density should be essentially identical to the critical value, a very peculiar situation which corresponds to a spatially flat universe. The existing data support this prediction. However, its biggest success is claimed to be the natural account for the emergence of the seeds of cosmic structure in terms of primordial quantum fluctuations, and the correct estimate of the corresponding microwave spectrum. This represents, thus, a situation which requires the combined application of general relativity (GR) and quantum theory, and that, moreover, is tied with observable imprints left from the early universe, in both the radiation in cosmic microwave background (CMB), and in the large scale cosmological structure we can observe today. It should not be surprising that, when dealing with attempts to apply our theories to the universe as a whole, we should come face to face with some of the most profound conceptual problems facing our current physical ideas. In fact, J. Hartle had noted long ago [28] that serious difficulties must be faced when attempting to apply quantum theory to cosmology, although the situations that were envisioned in those early works corresponded to the even more daunting problem of full quantum cosmology, and not the limited use of quantum theory to consider perturbative aspects, which is what is required in the treatment of the inflationary origin of the seeds of cosmic structure. This led him and his collaborators to consider the Consistent Histories framework, which is claimed to offer a version of quantum theory that does not rely on any fundamental notion of measurements, as the favored approach to use in such contexts. We will have a bit more to say about this shortly.
According to the theory of cosmic inflation, the large scale structures observed in our Universe (galaxies, clusters of galaxies, Cosmic Background Microwave—CMB—anisotropy…) are of quantum mechanical origin. They are nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic expansion and amplified by gravitational instability. At the end of inflation, these perturbations are placed in a two-mode squeezed state with the strongest squeezing ever produced in Nature (much larger than anything that can be made in the laboratory on Earth). This article studies whether astrophysical observations could unambiguously reveal this quantum origin by borrowing ideas from quantum information theory. It is argued that some of the tools needed to carry out this task have been discussed long ago by J. Bell in a, so far, largely unrecognized contribution. A detailled study of his paper and of the criticisms that have been put forward against his work is presented. Although J. Bell could not have realized it when he wrote his letter since the quantum state of cosmological perturbations was not yet fully characterized at that time, it is also shown that Cosmology and cosmic inflation represent the most interesting frameworks to apply the concepts he investigated. This confirms that cosmic inflation is not only a successful paradigm to understand the early Universe. It is also the only situation in Physics where one crucially needs General Relativity and Quantum Mechanics to derive the predictions of a theory and, where, at the same time, we have high-accuracy data to test these predictions, making inflation a playground of utmost importance to discuss foundational issues in Quantum Mechanics.
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.
We discuss here a not very well advertised problem afflicting the standard inflationary account of the origin of structure in the universe as the result of the, so called, quantum fluctuations of the inflaton field. We will show that such account is based on the properties of a quantum state that is homogeneous and isotropic, and that there is in the usual proposal no explanation for the emergence of inhomogeneities and anisotropies through a dynamics that preserves those symmetries in the quantum state. We will see that the issue can be seen as connected with the measurement problem in quantum mechanics, an unsatisfactory conceptual aspect of current quantum theory, which becomes intractable in the cosmological context at hand. We will see that one can address the issue adding the assumption that a new, and fundamental process in physics plays an essential role in this situation, (and naturally in other situations as well), and that unlike other cases, the cosmological problem at hand offers a path to investigate under empirical guidance some of the characteristics of this new physics.
Abstract The eternal inflation problem continues to be considered one of standard's cosmology most serious shortcomings. This arises when one considers the effects of “quantum fluctuations” on the zero mode of inflaton field during a Hubble time in the inflationary epoch. In the slow-roll regime it is quite clear that such quantum fluctuations could dwarf the classical rolling down of the inflaton, and with overwhelming probability this prevents inflation from ever ending. When one recognizes that quantum fluctuations can not be taken as synonymous of stochastic fluctuations, but rather intrinsic levels of indefiniteness in the quantities in question, one concludes that the eternal inflation problem simply does not exist. However, the same argument would serve to invalidate the account for the generation of the primordial seeds of cosmic structure as has been amply discussed elsewhere [1,2,3]. In order to do address that issue, one must explain the breaking of homogeneity and isotropy of the situation prevailing during the early inflationary epoch (at both the quantum and classical levels of the description). For that one needs to rely on some additional element, beyond those present in the traditional treatments. The so called spontaneous collapse theories offer a viable candidate for that element, namely the stochastic and spontaneous state reduction characteristic of those proposals possesses the basic features to break those symmetries. In fact, a version of the CSL theory adapted to the cosmological context has been shown to offer a satisfactory account for the origin the seeds of cosmic structure with an adequate power spectrum [2], and will serve as the basis of our analysis. However, once such stochastic collapse is introduced into the theoretical framework the eternal inflation problem has the potential reappear. In this manuscript we explore those issues in detail and discuss an avenue that seems to allow for a satisfactory account for the generation of the primordial inhomogeneities and anisotropies while freeing the theory from the eternal inflation problem.
The origin of cosmic acceleration remains a central problem in cosmology, commonly attributed to a cosmological constant within the ΛΛΛCDM model or to dynamical dark energy. Here, we develop an alternative approach in which acceleration emerges from quantum post-selection, a standard feature of quantum theory that is not usually incorporated into cosmological modelling. While quantum theory admits both pre-selected and post-selected ensembles, quantum cosmological models are almost exclusively formulated in terms of initial conditions. Building on previous work on post-selected quasiclassical dynamics, we construct a minimal predictive cosmological model in which post-selection and coarse-graining generate effective late-time acceleration without introducing a cosmological constant, dark energy, or modifications of general relativity. The resulting expansion history is highly constrained theoretically and depends on at most two parameters beyond standard Friedmann evolution. Confrontation with type Ia supernova and cosmic chronometer data yields statistically competitive fits while naturally avoiding the coincidence problem. The model also reproduces the standard radiation- and matter-dominated behaviour at early times and predicts a present-day jerk parameter significantly different from the ΛΛΛCDM value. These results suggest that cosmic acceleration may arise as a macroscopic quantum cosmological effect rather than from additional cosmological fluids or modified gravitational dynamics.
According to cosmological inflation, the inhomogeneities in our Universe are of quantum-mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum-to-classical transition, it remains to understand how a specific outcome can be produced in the early Universe, in the absence of any observer. The continuous spontaneous localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wave function collapse is caused by adding new nonlinear and stochastic terms to the Schr\"odinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wave function collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schr\"odinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with nS=4{n}_{\mathrm{S}}=4nS​=4, a spectral index in obvious contradiction with the cosmic microwave background anisotropy observations. The requirement that the non-scale-invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics. Due to the absence of a CSL amplification mechanism in field theory, this also has the consequence that the collapse mechanism of the inflationary fluctuations is not efficient. Then, we determine the collapse time. On small scales the collapse is almost instantaneous, and we recover exactly the behavior of the CSL harmonic oscillator (a case for which we present new results), whereas, on large scales, we find that the collapse is delayed and can take several e-folds to happen. We conclude that recovering the observational successes of inflation and, at the same time, reaching a satisfactory resolution of the inflationary ``macro-objectification'' issue seems problematic in the framework considered here. This work also provides a complete solution to the CSL parametric oscillator system, a topic we suggest could play a very important role to further constrain the CSL parameters. Our results illustrate the remarkable power of inflation and cosmology to constrain new physics.