  The aim of Quantum Fisher Cosmology is to use the quantum Fisher information
about pure de Sitter states to derive model independent observational
consequences of the existence of a primordial phase of the Universe of de
Sitter accelerated expansion. These quantum features are encoded in a scale
dependent quantum cosmological tilt that defines what we can call the de Sitter
universality class. The experimental predictions are: i) A phase transition
from red into blue tilt at a scale order $k= 1$ Mpc$^{-1}$ that naturally
solves the cosmological trans-Planckian problem, ii) A spectral index for
curvature fluctuations at CMB scales $k= 0.05$ Mpc$^{-1}$ equal to $0.0328$,
iii) A tilt running at scale $k=0.002$ Mpc$^{-1}$ equal to $-0.0019$, iv) An
enhancement of the amplitude of CMB peaks for extremely high multipoles ($l >
10^5$) that can provide a natural mechanism for primordial black hole formation
as a source of dark matter, v) A lack of power at scales of $8$ Mpc with
respect to the CMB scale that can explain the $\sigma_8$ tension.
