  The most robust prediction of inflationary cosmology is the existence of a
red tilt for the spectrum of curvature fluctuations that is experimentally of
order $0.04$. The tilt is derived solving the exact equation for quantum
fluctuations in a quasi de Sitter background defined by a equation of state
$\epsilon \equiv \frac{(p+\rho)}{\rho}$ with $\epsilon$ small but non
vanishing. The experimental data selects among the different quasi de Sitter
inflaton potentials. The origin of the lack of scale invariance associated with
the tilt is however classical in essence and parametrized by the slow roll of
the inflaton potential. Here we present a purely quantum mechanical and model
independent derivation of the tilt. This derivation is based on two basic
observations: first, the correlator for gauge invariant variables is related to
the {\it quantum Fisher function} measuring the quantum dependence of the
family of pure de Sitter vacua on the energy scale parameter; second, this
quantum Fisher function has a non vanishing scale dependent red tilt that, at
the energy scales of physical interest, fits the effective quasi de Sitter
prediction as well as the experimental value. This is a result that is model
independent and only based on the quantum features of the family of de Sitter
vacua.
