The trace left by signature-change-induced compactification

TL;DR

This paper investigates how signature oscillations in higher-dimensional models influence the effective dynamics of scalar fields, revealing a non-metric coupling that mimics a massive scalar field in four dimensions.

Contribution

It introduces a detailed analysis of scalar field dynamics on backgrounds with signature oscillations, highlighting the emergence of non-metric couplings in the effective four-dimensional theory.

Findings

Signature oscillations induce non-metric couplings in effective matter dynamics.

The effective scalar field behaves as a massive scalar in four dimensions.

The model provides insights into how microscopic signature changes affect macroscopic physics.

Abstract

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 average procedure, to an effective (''physical'') space-time 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 multidimensional FRW model, this structure is identical to a massive scalar field evolving in its homogeneous mode.