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Quantum Cosmology in Scalar-Tensorial Theories with Bohm-de Broglie Interpretation

Isaac Torres Sales

Published Mar 5, 2020• 0 citations
OpenAlex

Abstract

In this work, we both review and apply the formalism of Bohm-de Broglie interpretation of quantum mechanics to study two cosmological theories which modify Einstein’s general relativity through the introduction of a scalar field: the minimal and the non-minimal derivative couplings. We address some issues related to the quantization process in those theories, namely the ordering ambiguity and the problem of the quantization of Hamiltonians with non-integer powers in the momenta, in which case we apply a fractional derivative technique. We discuss how the Bohm-de Broglie interpretation provides us physical criteria to analyse the obtained results, specially with respect to the search for nonsingular solutions. With the help of those criteria, we discuss how the applied techniques are able to provide answers to the singularity problem, through bounces and cyclic universes.

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In this work, we both review and apply the formalism of Bohm-de Broglie interpretation of quantum mechanics to study two cosmological theories which modify Einstein’s general relativity through the introduction of a scalar field: the minimal and the non-minimal derivative couplings. We address some issues related to the quantization process in those theories, namely the ordering ambiguity and the problem of the quantization of Hamiltonians with non-integer powers in the momenta, in which case we apply a fractional derivative technique. We discuss how the Bohm-de Broglie interpretation provides us physical criteria to analyse the obtained results, specially with respect to the search for nonsingular solutions. With the help of those criteria, we discuss how the applied techniques are able to provide answers to the singularity problem, through bounces and cyclic universes.
We argue that the Copenhagen interpretation of quantum mechanics cannot be applied to quantum cosmology. Among the alternative interpretations, we choose to apply the Bohm-de Broglie interpretation of quantum mechanics to canonical quantum cosmology. For minisuperspace models, we show that there is no problem of time in this interpretation, and that quantum effects can avoid the initial singularity, create inflation and isotropize the Universe. For the general case, it is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures.
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 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 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.
We apply the de Broglie-Bohm interpretation to the Wheeler-DeWitt equation for the quantum FRW cosmological model with a minimal massless scalar field. We find that the quantum FRW cosmological model has quantum potential dominated solutions that avoid the initial and the final cosmological singularities. It is suggested that the quantum potential and the back-reaction of geometry and matter fields may change the property of the cosmological singularities of the Universe. 1 E-mail: sangkim@knusun1.kunsan.ac.kr 1 Introduction One of the most prominent classical-mechanical problems that quantum mechanics can solve is the classical singularity. For example, an electron of an atom suffers from the instability that due to the infinitely negative Coulomb potential and the electron in a zero-momentum state should fall into the infinite potential 2 . In quantum mechanics, however, the s-wavefunction (zero orbital angular momentum state) of the electron has zero probability at the singula...