Clocks, Algebras and Cosmology

Gauge invariant local observables describing primordial scalar quantum fluctuations in Inflationary Cosmology are identified as elements of a type $II$ de Sitter crossed product algebra. This algebra is defined, after adding a reference frame clock, as the algebra of clock dressed local operators. Clock dressing sets, in the weak gravity limit, the Schrodinger equation for gauge invariant quantum fluctuations. Instead of using a slow roll inflaton potential to define the clock Hamiltonian and the clock state we suggest a natural double de Sitter clock making the whole algebra associated with the planar patch a type $II$ factor. The corresponding clock states are EPR squeezed states. Using this clock to define the needed clock dressing leads to concrete model independent predictions of the inflationary parameters. Some speculative remarks on potential ways to define a type $I$ upgrading are briefly discussed.