  One of the most important achievements of inflationary cosmology is to
predict a departure from scale invariance of the power spectrum for scalar
curvature cosmological fluctuations. This tilt is understood as a consequence
of a quasi de Sitter classical equation of state describing the inflationary
dark energy dominated era. Here, following previous work, we find a departure
of scale invariance for the quantum Fisher information associated to de Sitter
vacuum for scalar quantum spectator modes. This gives rise to a purely quantum
cosmological tilt with a well defined dependence on energy scale. This quantum
tilt is imprinted, in a scale dependent energy uncertainty for the spectator
modes. The effective quasi de Sitter description of this model independent
energy uncertainty uniquely sets the effective quasi de Sitter parameters at
all energy scales. In particular, in the slow-roll regime characterized by an
almost constant $\epsilon$, the quantum Fisher -- model independent --
prediction for the spectral index is $(1-n_s) = 0.0328$ ($n_s=0.9672$).
Moreover, the energy scale dependence of the quantum cosmological tilt implies
the existence of a cosmological phase transition at energies higher than the
CMB scale where the tilt goes from red into blue. This strongly suggest the
existence of a pre-inflationary phase where the effective scalaron contributes
to the spectral index as normal relativistic matter and where the corresponding
growth of the power spectrum can result in dark matter in the form of small
mass primordial black holes. The source and features of the quantum
cosmological tilt leading to these predictions are determined by the
entanglement features of the de Sitter vacuum states.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology