$S$-Matrix and Anomaly of de Sitter

$S$-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.