A nonlinear quantum model of the Friedmann universe

Abstract

A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This leads to a quantisation scheme that yields a Schrodinger-type equation which is in general nonlinear in evolution. Nevertheless it is compatible with a probabilistic interpretation of quantum mechanics and in particular the construction of a Hilbert space with a Euclidean norm is possible. The new scheme is applied to the quantisation of a Friedmann Universe with a massive scalar field whose dynamical behaviour is investigated numerically.

11 pages of text + 4 pages for 8 figures

References in corpus (1)

• Quantum Gravity: a Progress Report

Cited by in corpus (4)

• Conformal geometrodynamics: True degrees of freedom in a truly canonical structure
• Hamiltonian formalism in Friedmann cosmology and its quantization
• Nonlinear quantum gravity on the constant mean curvature foliation
• An action principle for the quantization of parametric theories and nonlinear quantum cosmology