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Causal loop quantum cosmology in momentum space

Ali Shojai, Fatimah Shojai

Published Nov 26, 2012• 0 citations
OpenAlex

Abstract

We shall show that it is possible to make a causal interpretation of loop quantum cosmology using the momentum as the dynamical variable. We shall show that one can derive Bohmian trajectories. For a sample cosmological solution with cosmological constant, the trajectory is plotted. 1

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CAUSAL LOOP QUANTUM COSMOLOGY IN MOMENTUM SPACE

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Bohmian quantum gravity and cosmology

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Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.

arXiv:1801.03353•Jan 10, 2018•3 citations
Philosophers of science have not paid much attention to recent developments in quantum cosmology. This fact is surprising, since quantum cosmology is replete with conceptual issues involving (e.g.) the fundamental nature of time and space, the interpretation of quantum mechanics, and the ultimate meaning of probability. One notable exception, Quentin Smith, has recently examined the Hartle-Hawking (1983) proposal. Trying to make sense of the view, he resorts to an instrumentalist picture, which treats the proposal as merely a heuristic device for the algorithm responsible for predictions. While we do not examine Smith's account here, we would like to contrast it with the model presented in this note, in which a fully realistic interpretation of quantum cosmology is developed. Recently there has been a resurgence of interest in the de Broglie-Bohm causal interpretation of quantum mechanics.
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.
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.