Inflationary cosmology as flow of integrable weights

We identify the algebra of gauge invariant observables in de Sitter as the subalgebra of the type [Formula: see text] factor [Formula: see text] associated to de Sitter, defined as the centralizer of any integrable weight on [Formula: see text]. These algebras are for any integrable weight type [Formula: see text] 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 [Formula: see text] dS algebra cannot be represented as the [Formula: see text] limit (for [Formula: see text] 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 [Formula: see text] limit is algebraically nonexistent.