Signature change in loop quantum cosmology

TL;DR

This paper demonstrates that loop quantum cosmology naturally predicts a signature change from Lorentzian to Euclidean at high curvature, impacting cosmological perturbations and inflationary spectra, with potential links to quantum gravity theories.

Contribution

It shows that signature change emerges naturally in loop quantum cosmology due to quantum holonomies, providing a physical basis for the Hartle-Hawking proposal.

Findings

Signature change from Lorentzian to Euclidean in high curvature regimes.

Modified algebra of constraints affects propagation of perturbations.

Corrections to inflationary power spectra are derived.

Abstract

The Wick rotation is commonly considered only as an useful computational trick. However, as it was suggested by Hartle and Hawking already in early eighties, Wick rotation may gain physical meaning at the Planck epoch. While such possibility is conceptually interesting, leading to no-boundary proposal, mechanism behind the signature change remains mysterious. We show that the signature change anticipated by Hartle and Hawking naturally appear in loop quantum cosmology. Theory of cosmological perturbations with the effects of quantum holonomies is discussed. It was shown by Cailleteau \textit{et al.} (Class. Quant. Grav. {\bf 29} (2012) 095010) that this theory can be uniquely formulated in the anomaly-free manner. The obtained algebra of effective constraints turns out to be modified such that the metric signature is changing from Lorentzian in low curvature regime to Euclidean in high curvature regime. Implications of this phenomenon on propagation of cosmological perturbations are discussed and corrections to inflationary power spectra of scalar and tensor perturbations are derived. Possible relations with other approaches to quantum gravity are outlined. We also propose an intuitive explanation of the observed signature change using analogy with spontaneous symmetry breaking in "wired" metamaterials.