Cosmology without time: What to do with a possible signature change from quantum gravitational origin?

Within some approaches to loop quantum cosmology, the existence of an Euclidean phase at high density has been suggested. In this article, we try to explain clearly what are the observable consequences of this possible disappearance of time. Depending on whether it is a real fundamental effect or just an instability in the equation of motion, we show that very different conclusions should be drawn. We finally mention some possible consequences of this phenomenon in the black hole sector.