EFT Perspective On de-Sitter S-Matrix

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.

💡 Research Summary

The paper investigates how the well‑established analyticity properties of flat‑space scattering amplitudes can be transferred to a de Sitter (dS) background, where the lack of global time‑translation symmetry obstructs the usual definition of asymptotic “in” and “out” states. After reviewing the role of analyticity, unitarity, causality and Lorentz invariance in constraining low‑energy effective field theories (EFTs) via the flat‑space S‑matrix, the authors turn to recent constructions of a dS S‑matrix. Two versions are discussed: the Bunch‑Davies S‑matrix, defined with respect to the past conformal infinity, and the Unruh‑DeWitt S‑matrix, defined with respect to a future horizon. Both are obtained by amputating time‑ordered correlation functions in a manner analogous to the LSZ reduction formula, but with mode functions appropriate to the expanding dS geometry.

The core technical result is a double‑limit relation that connects a dS 2→2 amplitude (A_{2\to2}) to the flat‑space amplitude (M_{2\to2}^{\text{flat}}(s)). The limit consists of sending the Hubble scale (H\to0) (the “flat‑space limit”) while simultaneously taking the total external energy (E\to0) but keeping the ratio (E/H) finite. In this regime the dS amplitude simplifies to \