Non-differentiable Degrees of Freedom : Fluctuating Metric Signature

Details Non-differentiable Degrees of Freedom : Fluctuating Metric Signature Non-differentiable Degrees of Freedom : Fluctuating Metric Signature

2000-05-29

arxiv.org/abs/gr-qc/0005123v2

Class.Quant.Grav. 18 (2001) 1787-1798

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

unessential changes

Scientific paper

10.1088/0264-9381/18/9/312

In this article we investigate the metric signature as a non-differentiable ({\it i.e.} discrete as opposed to continuous) degree of freedom. The specific model is a vacuum 7D Universe on the principal bundle with an SU(2) structural group. An analytical solution is found which to a 4D observer appears as a flat Universe with a fluctuating metric signature, and frozen extra dimensions with an SU(2) instanton gauge field. A piece of this solution with linear size of the Planck length ($\approx l_{Pl}$) can be considered as seeding the quantum birth of a regular Universe. A boundary of this piece can initiate the formation of a Lorentzian Universe filled with the gauge fields and in which the extra dimensions have been ``frozen''.

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