EFT Perspective On de-Sitter S-Matrix

TL;DR

This paper explores the relationship between flat-space and de Sitter S-matrices, deriving a limit where flat-space analyticity properties inform de Sitter EFTs, and uncovers connections to special scalar theories like DBI and Galileons.

Contribution

It establishes a specific limit linking flat-space and de Sitter S-matrices, and identifies conditions under which de Sitter EFTs reduce to known special scalar theories.

Findings

Derived a relationship between flat-space and de Sitter S-matrices in a certain limit.

Identified a connection between de Sitter S-matrix properties and exceptional EFTs.

Rediscovered DBI and Galileon theories through energy conservation constraints.

Abstract

Non-perturbative limitations on low-energy effective field theories (EFTs) based on the characteristics of high-energy theory are provided by the analyticity of the flat-space version of the S-matrix. Although the analyticity of the flat-space S-matrix is widely established, it is difficult to apply this framework to de Sitter space because the growing backdrop breaks time-translation symmetry and makes it more difficult to define asymptotic states. The flat-space analyticity imprint on the de Sitter S-matrix is examined in this study. On a certain limit, we derive a comprehensive relationship between the flat-space amplitude and the de Sitter S-matrix. In particular, we demonstrate that the relationship is valid for tree-level amplitude exchanging with arbitrary local derivative interactions with a large scalar field. Next, we contend that this specific limit is more consistent with the definition of EFT since, similar to flat space, the Mandelstam variable may be identified as the unique energy scale because the total energy dependence of the de Sitter S-matrix becomes negligible. Finally, we also find an unexpected connection between the idea of generalized energy conservation of an S-matrix of four-dimensional de Sitter and exceptional EFTs in de Sitter space. We restrict the coupling constants in theories of self-interacting scalars dwelling in the exceptional series of de Sitter representations by requiring that such an S-matrix only has support when the total energies of in and out states are equal. We rediscover the Dirac-Born-Infeld (DBI) and Special Galileon theories, in which a single coupling constant uniquely fixes the four-point scalar self-interactions.