In this paper, we consider the De Broglie–Bohm interpretation of a Hořava–Lifshitz quantum cosmology model in the presence of a radiation perfect fluid. We compute the Bohm’s trajectory for the scale factor and show that it never goes to zero. That result gives a strong indication that this model is free from singularities at the quantum level. We also compute the quantum potential. That quantity helps in understanding why the scale factor never vanishes.
In this paper, we consider the De Broglie–Bohm interpretation of a Hořava–Lifshitz quantum cosmology model in the presence of a radiation perfect fluid. We compute the Bohm’s trajectory for the scale factor and show that it never goes to zero. That result gives a strong indication that this model is free from singularities at the quantum level. We also compute the quantum potential. That quantity helps in understanding why the scale factor never vanishes.
Recently it has been claimed that the Wheeler--DeWitt quantization of gravity is unable to avoid cosmological singularities. However, in order to make this assertion, one must specify the underlying interpretation of quantum mechanics which has been adopted. For instance, several nonsingular models were obtained in Wheeler--DeWitt quantum cosmology in the framework of the de Broglie--Bohm quantum theory. Conversely, there are specific situations where the singularity cannot be avoided in the framework of the consistent histories approach to quantum mechanics. In these specific situations, the matter content is described by a scalar field, and the Wheeler--DeWitt equation looks like a Klein--Gordon equation. The aim of this work is to study a possible singular behavior of quantum cosmological models in which the matter content is described by a hydrodynamical perfect fluid, where the resulting wave equation is a genuine Schr\"odinger equation. In this case, it is shown that the conclusions of the consistent histories and the de Broglie--Bohm approaches coincide in the quantum cosmological models where the curvature of the spatial sections is not positive definite, namely, that the cosmological singularities are eliminated. In the case of positive spatial curvature, the family of histories is no longer consistent, and no conclusion can be given in this framework.
In the isotropic quantum cosmological perfect fluid model, the initial singularity can be avoided, while the classical behaviour is recovered asymptotically. We verify if initial anisotropies can also be suppressed in a quantum version of a classical anisotropic model where gravity is coupled to a perfect fluid. Employing a Bianchi I cosmological model, we obtain a "Schrödinger-like" equation where the matter variables play de role of time. This equation has a hyperbolic signature. It can be explicitly solved and a wave packet is constructed. The expectation value of the scale factor, evaluated in the spirit of the many-worlds interpretation, reveals an isotropic Universe. On the other hand, the bohmian trajectories indicate the existence of anisotropies. This is an example where the Bohm-de Broglie and the many-worlds interpretations are not equivalent. It is argued that this inequivalence is due to the hyperbolic structure of the "Schrödinger-like" equation.
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 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...
We apply the complex de Broglie–Bohm formulation of quantum mechanics in Chou and Wyatt (Phys Rev A 76: 012115, 2007 ), Gozzi (Phys Lett B 165: 351, 1985 ), Bhalla et al. (Am J Phys 65: 1187, 1997 ) to a spatially closed homogeneous and isotropic early universe whose matter contents are radiation and dust perfect fluids. We then show that an expanding classical universe can emerge from an oscillating (with complex scale factor) quantum universe without singularity. Furthermore, the universe obtained in this process has no horizon or flatness problems.
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.