Inflationary Cosmology as flow of integrable weights

TL;DR

This paper explores the algebraic structure of gauge invariant observables in de Sitter space, defining inflationary cosmology as a flow of integrable weights and showing the non-existence of a pure de Sitter algebra as a limit of inflationary models.

Contribution

It introduces a novel algebraic framework for inflationary cosmology using integrable weights and analyzes the limitations of representing de Sitter algebra as a limit of inflationary models.

Findings

Type II₁ de Sitter algebra cannot be obtained as an ε→0 limit of gauge invariant algebras.

Pure de Sitter algebra at ε=0 is algebraically non-existent.

Inflationary cosmology is characterized as a flow of integrable weights.

Abstract

We identify the algebra of gauge invariant observables in de Sitter as the subalgebra of the type $III_1$ 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 $II_{\infty}$ 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 $II_1$ 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.