$S$-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.
