  We suggest a new conceptual frame where inflationary Cosmology is quantum
mechanically described using the Hilbert space representation of the crossed
product of the type $III$ factor associated with the algebra of local operators
on the de Sitter static patch and the automorphism of translations in the
emergent conformal time. In this formal framework scalar curvature fluctuations
are determined by the gravitational potential induced by the quantum variance
of the generator of the conformal time automorphisms. Choosing as
representative, in the Hilbert space of the crossed product, the effective
vacuum state for each mode and conformal time, we evaluate the quantum variance
and the induced scalar curvature fluctuations. This leads to a model
independent characterization of the inflationary parameters (1-n_s) \sim 0.0318
and \epsilon\sim 0.0027 in good agreement with Planck experimental results. In
this formal frame inflation extends the algebra of observables in a primordial
dS expanding Universe. In this extension time evolution becomes an inner
automorphism and the conjugated energy fluctuations manifest as the observable
scalar curvature fluctuations.
