Inflationary Cosmology as flow of integrable weights

We identify the algebra of gauge invariant observables in de Sitter as the subalgebra of the type $II{I}_1$ factor $A_{dS}$, associated to de Sitter, defined as the centralizer of any integrable weight on $A_{dS}$. These algebras are for any integrable weight type $I{I}_{\mathrm{\infty }}$ factors admitting a crossed product representation with respect to modular automorphisms. In this context we define Inflationary Cosmology as the flow of integrable weights and the dual automorphism as the flow generator. Using some basic properties of integrable weights we show that any type $I{I}_1$ dS algebra cannot be represented as the $\epsilon =0$ limit ( for $\epsilon$ the slow roll parameter ) of the gauge invariant algebra defined by any integrable weight. This strongly indicates that the pure dS algebra defined as the $\epsilon =0$ limit is algebraically non existent.