Quantum cosmology from the de Broglie–Bohm perspective

Abstract

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 deBroglie-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.

A critical review of classical bouncing cosmologies

“…A proposal to circumvent this problem consists of assuming a trajectory formulation of quantum mechanics [114,115] in which the scale factor follows specific trajectory values [116]. Applying this formalism and assuming regular boundary conditions, one finds that all possible trajectories are nonsingular and include a bounce [117] (see also [118] for a different but related approach).…”

“…Of course, all known formulations of quantum mechanics being strictly equivalent, the fact that the universe underwent a regular bouncing phase or not should not depend on which formulation one picks, so it is reasonable to expect that the results obtained in Refs. [116,118] generically indicate that it is canonical quantum gravity itself which allows for a bounce to take place.…”

Classical universe emerging from quantum cosmology without horizon and flatness problems

“…in particular [47]). As far as the usual dBB approach to quantum cosmology is concerned, linear cosmological perturbations have been considered (see the references in [48][49][50][51]). Falsifiable observational consequences were pointed out and some fitted with known data, although others remain to be tested.…”

“…To find a solution to the above mentioned problems via quantum cosmology, a straightforward and direct way could be the de Broglie-Bohm (dBB), or causal stochastic, interpretation of quantum cosmology. The dBB interpretation is favorable, especially for a quantum theory of cosmology, because this interpretation is able to resolve the above mentioned conceptual problems of quantum cosmology [4][5][6][7][8]. However, we have a problem in using a e-mail: s-jalalzadeh@sbu.ac.ir b e-mail: pmoniz@ubi.pt the dBB interpretation in quantum cosmology.…”

The quantum state of the universe from deformation quantization and classical-quantum correlation

“…It dose not explain the apparent collapse after the measurement is completed, or why all but one of the diagonal elements of the density matrix become null when the measurement is finished [7]. Also, in its developments like the consistence histories approach [8] the important role played by observers is not yet explained [9] and it is not clear how to describe a quantum universe when the background geometry is not classical [10]. Nevertheless, there are some alternative solutions to the above quantum cosmological difficulties, which together with decoherence may solve the measurement problem maintaining the universality of quantum theory and emergence of classical universe.…”