A nonlinear quantum model of the Friedmann universe

Details A nonlinear quantum model of the Friedmann universe A nonlinear quantum model of the Friedmann universe

2003-04-29

arxiv.org/abs/gr-qc/0304101v8

Class.Quant.Grav. 20 (2003) 3151-3164

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages of text + 4 pages for 8 figures

Scientific paper

10.1088/0264-9381/20/14/316

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.

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