Imprints of flat space analyticity in de Sitter S-matrix

TL;DR

This paper explores how the well-understood analytic structure of flat-space S-matrix theory influences the de Sitter S-matrix, especially in the Hubble flat-space limit, revealing new insights into effective field theories in expanding universes.

Contribution

It establishes a relation between flat-space and de Sitter S-matrices in a specific limit, extending flat-space analyticity concepts to de Sitter space for tree-level scalar exchanges.

Findings

Derived a relation between flat-space and de Sitter S-matrices in the Hubble flat-space limit.

Showed the relation holds for tree-level amplitude with massive scalar exchange and local derivative interactions.

Argued the Hubble flat-space limit aligns with effective field theory descriptions in de Sitter space.

Abstract

The analytic structure of the flat-space S-matrix provides non-perturbative constraints on low-energy effective field theories based on the properties of high-energy theory. While the analytic structure of the flat-space S-matrix is well understood, extending this framework to de Sitter space is challenging, as the expanding background complicates the definition of asymptotic states and breaks time-translation symmetry. This paper investigates how flat-space analyticity is imprinted on the de Sitter S-matrix. We derive a relation between flat-space amplitude and de Sitter S-matrix on a specific limit called the Hubble flat-space limit. Specifically, we show that the relation holds for tree-level amplitude exchanging a massive scalar field with any local derivative interactions. Finally, we argue that the Hubble flat-space limit is more compatible with the description of effective field theory, as the total energy dependence of de Sitter S-matrix becomes trivial, allowing the Mandelstam variable to be identified as the unique energy scale, just as in flat space.