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Quantum cosmology with varying speed of light and Bohmian trajectories

Fatimah Shojai, Saeid Molladavoudi

Published Nov 26, 2012• 8 citations
OpenAlex

Abstract

The classical trajectories for FLRW universe with varying speed of light are obtained for the cases in which the cosmological constant depends or not depend on the velocity of light. The theory is then quantized and the corresponding WDW equation is solved. It is shown that the method of causal interpretation of Bohm can be applied successfully to the theory. Finally the Bohmian trajectories are obtained and compared with the classical ones. 1 1

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The classical trajectories for FLRW universe with varying speed of light are obtained for the cases in which the cosmological constant depends or not depend on the velocity of light. The theory is then quantized and the corresponding WDW equation is solved. It is shown that the method of causal interpretation of Bohm can be applied successfully to the theory. Finally the Bohmian trajectories are obtained and compared with the classical ones. 1 1
The quantized Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) model minimally coupled to a free massless scalar field is studied and interpreted in the Bohm-de Broglie framework. We analyze the quantum bohmian trajectories corresponding to a certain class of gaussian packets, solutions of the Wheeler-DeWitt equation. We show that these bohmian trajectories undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period. It is shown that the luminosity-redshift relation in the quantum cosmological model can be made close to the corresponding relation coming from the classical model suplemented by a cosmological constant, for z<1z<1z<1. In this way we have the posibility of interpreting the present observations of high redshift supernovae as the consequence of a quantum cosmological effect.
ABSTRACT We present a theoretical analysis of the WDW approach to quantum cosmology extended to gravity theories with torsion. The dynamics of the FLRW universe is formulated as a classical Hamiltonian problem of point particle mechanics. Unlike in the WDW formalism, the Hamiltonian is not zero, though, and the third quantization does not enforce the cosmic time to vanish. The wave function of the Universe appears as a superposition of eigenfunctions of the quantum Hamiltonian with the cosmic time being the conjugate to its eigenvalues, spatial curvatures. The notion of weak measurement is then introduced to avoid the collapse of the total universal wave function upon measurements of the parameter set describing matter and spacetime. The collapse postulate of the standard Copenhagen quantum theory is discussed and the de Broglie–Bohm interpretation of the effective wave function introduced. The question of the boundary conditions for both, the wave function and the Bohmian guidance equation, is addressed. The corresponding numerical calculations will be published in a separate paper.
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.