Signature change in loop quantum cosmology

Abstract

TheWick rotation is commonly considered only as a useful computational trick. However, as 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 appears in loop quantum cosmology. Theory of cosmological perturbations with the effects of quantum holonomies is discussed. It was shown by Cailleteau et al. [3] that this theory can be uniquely formulated in an anomaly-free manner. The obtained algebra of effective constraints turns out to be modified so 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.