$S$-Matrix and Anomaly of de Sitter

TL;DR

This paper explores how the $S$-matrix formulation of gravity constrains de Sitter vacua, linking quantum anomalies and corpuscular effects to resolve cosmological puzzles and suggesting observable signatures in theories with many particle species.

Contribution

It introduces a novel connection between $S$-matrix constraints, quantum anomalies, and corpuscular effects in de Sitter space within string theory and quantum gravity.

Findings

De Sitter vacua are incompatible with $S$-matrix formulation unless trivialized.

Quantum break-time is proportional to inverse gravitational and string couplings.

Large number of particle species can amplify primordial quantum imprints.

Abstract

$S$-matrix formulation of gravity excludes de Sitter vacua. In particular, this is organic to string theory. The $S$-matrix constraint is enforced by an anomalous quantum break-time proportional to the inverse values of gravitational and/or string couplings. Due to this, de Sitter can satisfy the conditions for a valid vacuum only at the expense of trivializing the graviton and closed-string $S$-matrixes. At non-zero gravitational and string couplings, de Sitter is deformed by corpuscular $1/N$ effects, similarly to Witten-Veneziano mechanism in QCD with $N$ colors. In this picture, an $S$-matrix formulation of Einstein gravity, such as string theory, nullifies an outstanding cosmological puzzle. We discuss possible observational signatures which are especially interesting in theories with large number of particle species. Species can enhance the primordial quantum imprints to potentially observable level even if the standard inflaton fluctuations are negligible.