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arXiv:0804.4656

De Broglie-Bohm Prediction of Quantum Violations for Cosmological Super-Hubble Modes

Antony Valentini

Published Apr 29, 2008• 18 citations
arXivHTMLPDF

Abstract

The hypothesis of quantum nonequilibrium at the big bang is shown to have observable consequences. For a scalar field on expanding space, we show that relaxation to quantum equilibrium (in de Broglie-Bohm theory) is suppressed for field modes whose quantum time evolution satisfies a certain inequality, resulting in a 'freezing' of early quantum nonequilibrium for these particular modes. For an early radiation-dominated expansion, the inequality implies a corresponding physical wavelength that is larger than the (instantaneous) Hubble radius. These results make it possible, for the first time, to make quantitative predictions for nonequilibrium deviations from quantum theory, in the context of specific cosmological models. We discuss some possible consequences: corrections to inflationary predictions for the cosmic microwave background, non-inflationary super-Hubble field correlations, and relic nonequilibrium particles.

DOI
10.48550/arxiv.0804.4656

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The hypothesis of quantum nonequilibrium at the big bang is shown to have observable consequences. For a scalar field on expanding space, we show that relaxation to quantum equilibrium (in de Broglie-Bohm theory) is suppressed for field modes whose quantum time evolution satisfies a certain inequality, resulting in a 'freezing' of early quantum nonequilibrium for these particular modes. For an early radiation-dominated expansion, the inequality implies a corresponding physical wavelength that is larger than the (instantaneous) Hubble radius. These results make it possible, for the first time, to make quantitative predictions for nonequilibrium deviations from quantum theory, in the context of specific cosmological models. We discuss some possible consequences: corrections to inflationary predictions for the cosmic microwave background, non-inflationary super-Hubble field correlations, and relic nonequilibrium particles.
We show that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances and at very early times. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with nonstandard field fluctuations (``quantum nonequilibrium''). We show that inflationary expansion can transfer microscopic nonequilibrium to macroscopic scales, resulting in anomalous power spectra for the cosmic microwave background. The conclusions depend only weakly on the details of the de Broglie-Bohm dynamics. We discuss, in particular, the nonequilibrium breaking of scale invariance for the primordial (scalar) power spectrum. We also show how nonequilibrium can generate primordial perturbations with nonrandom phases and intermode correlations (primordial non-Gaussianity). We address the possibility of a low-power anomaly at large angular scales, and show how it might arise from a nonequilibrium suppression of quantum noise. Recent observations are used to set an approximate bound on violations of quantum theory in the early Universe.
Quantum mechanics is a highly successful fundamental theory which has passed every experimental test to date. Yet standard quantum mechanics fails to provide an adequate description of measurement processes, which has long been rationalized with operationalist and positivist philosophical arguments but is nevertheless a serious shortfall in a fundamental theory. In this dissertation we introduce quantum mechanics with a discussion of the measurement problem. We then review the de Broglie-Bohm pilot-wave formulation, a nonlocal hidden-variables theory where the state of a quantum system is described by a configuration (independent of measurements) in addition to the wave function, and we apply it to fundamental problems concerning black holes and the early universe.\nIn de Broglie-Bohm theory, general initial conditions allow for deviations from the statistical predictions of standard quantum mechanics. We review how the Born rule can be understood as the result of an equilibration process for systems with sufficient mixing before proceeding to study the implications of quantum nonequilibrium in various physical contexts.\nIn this work we show that small perturbations to a system are themselves insufficient to drive relaxation to quantum equilibrium even over very long timescales. This has implications for the potential survival of nonequilibrium in relic particles, and renders it unlikely that field perturbations can be driven to equilibrium by small corrections to the Bunch-Davies vacuum during inflation, allowing for the possible detection of imprints of nonequilibrium in the cosmic microwave background. Using a simple model we also demonstrate how quantum nonequilibrium can propagate nonlocally through entanglement, providing a mechanism for information flow from black holes. This opens up a possible path to the resolution of the black hole information paradox by allowing for information to be released in hidden variable degrees of freedom during black hole evaporation. Finally, we consider whether features in the angular power spectrum of temperature anisotropies in the cosmic microwave background radiation could arise from quantum nonequilibrium initial conditions. Preliminary results indicate that this approach can provide a natural explanation for the power deficit anomaly at large angular scales, as well as oscillatory features in the same regime.
We present an exactly solvable model for the suppression of quantum noise at large scales on expanding space. The suppression arises naturally in the de Broglie-Bohm pilot-wave formulation of quantum theory, according to which the Born probability rule has a dynamical origin. For a scalar field on a radiation-dominated background we construct the exact solution for the time-evolving wave functional and study properties of the associated field trajectories. It is shown that the time evolution of a field mode on expanding space is mathematically equivalent to that of a standard harmonic oscillator with a ``retarded time'' that depends on the wavelength of the mode. In the far super-Hubble regime the equivalent oscillator evolves over only one Hubble time, yielding a simple mechanism whereby relaxation to the Born rule can be suppressed on very large scales. We present numerical simulations illustrating how the expansion of space can cause a retardation of relaxation in the super-Hubble regime. Given these results it is natural to expect a suppression of quantum noise at super-Hubble wavelengths. Such suppression could have taken place in a preinflationary era, resulting in a large-scale power deficit in the cosmic microwave background.
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.
The de Broglie–Bohm pilot-wave formulation of quantum theory allows the existence of physical states that violate the Born probability rule. Recent work has shown that in pilot-wave field theory on expanding space relaxation to the Born rule is suppressed for long-wavelength field modes, resulting in a large-scale power deficit [Formula: see text] which for a radiation-dominated expansion is found to have an approximate inverse-tangent dependence on [Formula: see text] (assuming that the width of the initial distribution is smaller than the width of the initial Born-rule distribution and that the initial quantum states are evenly-weighted superpositions of energy states). In this paper, we show that the functional form of [Formula: see text] is robust under changes in the initial nonequilibrium distribution — subject to the limitation of a subquantum width — as well as under the addition of an inflationary era at the end of the radiation-dominated phase. In both cases, the predicted deficit [Formula: see text] remains an inverse-tangent function of [Formula: see text]. Furthermore, with the inflationary phase the dependence of the fitting parameters on the number of superposed pre-inflationary energy states is comparable to that found previously. Our results indicate that, for the assumed broad class of initial conditions, an inverse-tangent power deficit is likely to be a fairly general and robust signature of quantum relaxation in the early universe.
We study incomplete relaxation to quantum equilibrium at long wavelengths, during a preinflationary phase, as a possible explanation for the reported large-scale anomalies in the cosmic microwave background. Our scenario makes use of the de Broglie--Bohm pilot-wave formulation of quantum theory, in which the Born probability rule has a dynamical origin. The large-scale power deficit could arise from incomplete relaxation for the amplitudes of the primordial perturbations. We show, by numerical simulations for a spectator scalar field, that if the preinflationary era is radiation dominated then the deficit in the emerging power spectrum will have a characteristic shape (an inverse-tangent dependence on wave number kkk, with oscillations). It is found that our scenario is able to produce a power deficit in the observed region and of the observed (approximate) magnitude for an appropriate choice of cosmological parameters. We also discuss the large-scale anisotropy, which might arise from incomplete relaxation for the phases of the primordial perturbations. We present numerical simulations for phase relaxation, and we show how to define characteristic scales for amplitude and phase nonequilibrium. The extent to which the data might support our scenario is left as a question for future work. Our results suggest that we have a potentially viable model that might explain two apparently independent cosmic anomalies by means of a single mechanism.