THE TRACE LEFT BY SIGNATURE-CHANGE-INDUCED COMPACTIFICATION

Recently, it has been shown that an infinite succession of classical signature changes ('signature oscillations') can compactify and stabilize internal dimensions, and simultaneously leads, after a coarse graining type of averaging procedure, to an effective ('physical') spacetime geometry displaying the usual Lorentzian metric signature. Here, we consider a minimally coupled scalar field on such an oscillating background and study its effective dynamics. It turns out that the resulting field equation in four dimensions contains a coupling to some non-metric structure, the imprint of the 'microscopic' signature oscillations on the effective properties of matter. In a multi-dimensional FRW model, this structure is identical to a massive scalar field evolving in its homogeneous mode.