<i>S</i>-Matrix and Anomaly of de Sitter
Gia Dvali
Abstract
<i>S</i>-matrix formulation of gravity excludes de Sitter vacua. In particular, this is organic to string theory. The <i>S</i>-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 <i>S</i>-matrices. At non-zero gravitational and string couplings, de Sitter is deformed by corpuscular <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><mi>N</mi></mrow></semantics></math></inline-formula> effects, similarly to Witten–Veneziano mechanism in QCD with <i>N</i> colors. In this picture, an <i>S</i>-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 a large number of particle species. Species can enhance the primordial quantum imprints to potentially observable level even if the standard inflaton fluctuations are negligible.