Quantum Fisher Cosmology: Confronting Observations and the Trans-Planckian Problem

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.