Quantum and Classical Cosmology in the Brans–Dicke Theory

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω<−32, the energy is bounded from below and singularity-free solutions are found. However, in the case ω>−32, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of ω.

De Broglie–Bohm interpretation of a Hořava–Lifshitz quantum cosmology model

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.

The spatially flat Friedmann equation for early rainbow universe

We derive the spatially flat rainbow-Friedmann equation from de Broglie–Bohm interpretation in canonical quantum cosmology. Our result shows that the spatially flat rainbow-Friedmann equations of early and late-time universe are having different forms. The spatially flat rainbow-Friedmann equation of early universe which is obtained in this paper is quite different from the one which was initially derived by Magueijo and Smolin [Class. Quantum Grav. 21, 1725 (2004)]. However, the spatially flat rainbow-Friedmann equation for late-time universe obtained in this paper is found to be the same as the one derived by Magueijo and Smolin (for the case [Formula: see text] and Newton’s gravitational constant [Formula: see text]. The new spatially flat rainbow-Friedmann equation obtained in this paper could provide an alternative way in understanding the evolution of the early rainbow universe.

Measurement in the de Broglie-Bohm Interpretation: Double-Slit, Stern-Gerlach, and EPR-B

We propose a pedagogical presentation of measurement in the de Broglie-Bohm interpretation. In this heterodox interpretation, the position of a quantum particle exists and is piloted by the phase of the wave function. We show how this position explains determinism and realism in the three most important experiments of quantum measurement: double-slit, Stern-Gerlach, and EPR-B. First, we demonstrate the conditions in which the de Broglie-Bohm interpretation can be assumed to be valid through continuity with classical mechanics. Second, we present a numerical simulation of the double-slit experiment performed by Jönsson in 1961 with electrons. It demonstrates the continuity between classical mechanics and quantum mechanics. Third, we present an analytic expression of the wave function in the Stern-Gerlach experiment. This explicit solution requires the calculation of a Pauli spinor with a spatial extension. This solution enables us to demonstrate the decoherence of the wave function and the three postulates of quantum measurement. Finally, we study the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time shows that a causal interpretation exists where each atom has a position and a spin.