The quantum cosmological tilt and the origin of dark matter

A promising candidate for cold dark matter is primordial black holes (PBH) formed from strong primordial quantum fluctuations. A necessary condition for the formation of PBH's is a change of sign in the tilt governing the anomalous scale invariance of the power spectrum from red at large scales into blue at small scales. Non-perturbative information on the dependence of the power spectrum tilt on energy scale can be extracted from the quantum Fisher information measuring the energy dependence of the quantum phases defining the de Sitter vacua. We show that this non-perturbative quantum tilt goes from a red tilted phase, at large scales, into a blue tilted phase at small scales converging to $n_s=2$ in the UV. This allows the formation of PBH's in the range of masses $\lesssim 10^{20} gr$.