  In inflationary cosmology the quasi de Sitter graceful exit allows us to
measure the quantum features of the primordial dS phase, in particular, the
lack of scale invariance parametrized by the spectral index $n_s$. In this
review we summarize previous work on how the underlying primordial scaling law
is implemented in the dS quantum Fisher information of the dS planar ground
state (dSQFI). At large scales the dSQFI unequivocally sets, without any qdS
input, the value of $n_s$ to be $0.9672$. This value is independent of the
tensor to scalar ratio whose value requires model dependent input. In addition
the dSQFI predicts, at large scales, a small running compatible with the
current experimental results. Other phenomenological consequences of the dSQFI
for small scales, will be discussed in a future review.
