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International Journal of Modern Physics A

Quantum Bohmian description of a primordial universe with Fermionic and Bosonic sources

Marlos O. Ribas, F. P. Devecchi, Gilberto Medeiros Kremer

Published May 27, 2021• 1 citation
Publisher

Abstract

We present a model of an early universe where the sources of gravitational effects are a scalar field, a relativistic fluid based on Schutz’s model and a self-interacting fermionic field. From the classical analysis based on the Hamiltonian formalism we show that the scale factor of the universe can be expressed in terms of a conformal time that emerges from the fluid’s degrees of freedom. From the Wheeler–DeWitt equation, a wave packet solution as function of the conformal time is determined. It is shown that the combination of the scalar and the fermionic field furnishes a consistent quantum regime and a smooth transition to the classical description, working with the aid of the Bohmian mechanics and in particular with the concept of quantum potential. The influence of the presence of the scalar field is also discussed.

DOI
10.1142/s0217751x21501037

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We present a model of an early universe where the sources of gravitational effects are a scalar field, a relativistic fluid based on Schutz’s model and a self-interacting fermionic field. From the classical analysis based on the Hamiltonian formalism we show that the scale factor of the universe can be expressed in terms of a conformal time that emerges from the fluid’s degrees of freedom. From the Wheeler–DeWitt equation, a wave packet solution as function of the conformal time is determined. It is shown that the combination of the scalar and the fermionic field furnishes a consistent quantum regime and a smooth transition to the classical description, working with the aid of the Bohmian mechanics and in particular with the concept of quantum potential. The influence of the presence of the scalar field is also discussed.
We construct a Bohmian quantum cosmological model for a spatially flat Friedmann-Robertson-Walker universe filled with a single scalar field whose potential provides a unified description of cold dark matter and dark energy at the background level. Starting from the Einstein-Hilbert action supplemented by a scalar field, we derive the minisuperspace Lagrangian and the associated canonical Hamiltonian formulation. By means of a nontrivial canonical transformation, the minisuperspace dynamics is mapped into that of a two-dimensional hyperbolic oscillator with a fixed frequency ratio, rendering the Wheeler-DeWitt equation exactly solvable by separation of variables. The resulting Wheeler-DeWitt solutions are expressed in terms of parabolic cylinder functions and are parametrised by a continuous separation constant, reflecting the constrained nature of the theory and the absence of a standard Schrödinger time parameter. Adopting the de Broglie-Bohm formulation, we derive deterministic guidance equations in minisuperspace and construct a well-defined Bohmian Hubble parameter directly in terms of the pilot-wave phase. Finally, we present a Wheeler-DeWitt-derived toy wave function for which the Bohmian trajectories and the associated cosmological expansion history can be obtained analytically, reproducing the late-time ΛCDM behaviour while exhibiting quantum modifications at earlier epochs.
Abstract In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of an alternative non-trivial ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. The Wheeler–DeWitt equation has a contribution from the change in factor ordering, hence there are new quantum effects. We compare the results between the non-trivial and the trivial ordering cases, showing that the classical limit is valid for both orderings, but new bouncing and cyclic solutions are present in the non-trivial case. Additionally, we show that the non-singular solutions already present in the trivial ordering formalism keep valid.
We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of ‘canonical ’ wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wave packets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from de-Broglie Bohm interpretation of quantum mechanics to recover the notion of time and compare the classical and Bohmian results. We exhibit that the usage of the canonical prescription and appropriate choices of expansion coefficients result in the suppression of the quantum potential and coincidence between classical and Bohmian results. We show that, in some cases, contrary to Friedmann-Robertson-Walker case, the bound state solutions also exist for all positive values of the cosmological constant. Pacs: 98.80.Qc, 04.40.Nr, 04.60.Ds; 1
Abstract We derive the quantum Einstein equations (which are the quantum generalisation of the Einstein equations of classical gravity) from Bohmian quantum gravity. Bohmian quantum gravity is a non-classical geometrodynamics (in the ADM formalism) which describes the time evolution of a three-geometry and of a matter field (or other matter degrees of freedom) on a three manifold. The evolution is determined by a velocity law which is defined by the wave function. The wave function itself satisfies the Wheeler–DeWitt equation. We cast the Bohmian dynamics into the form of the Einstein field equations, where the interesting novelty is a contribution to the energy–momentum tensor that depends on the quantum potential.
We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of 'canonical' wavepackets resulting from the solutions of a class of Wheeler–DeWitt equations in the Stephani Universe. We suggest appropriate initial conditions which result in wavepackets containing some desirable properties, most importantly good classical and quantum correspondence. We also study the situation from the de Broglie–Bohm interpretation of quantum mechanics viewpoint to recover the notion of time and compare the classical and Bohmian results. We show the usage of the canonical prescription and appropriate choices of expansion coefficients to result in the suppression of the quantum potential and coincidence of classical and Bohmian results. We show that, in some cases, contrary to the Friedmann–Robertson–Walker case, the bound state solutions also exist for all positive values of the cosmological constant.