Signature change in loop quantum cosmology
  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.
