{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T00:04:12Z","timestamp":1782518652816,"version":"3.54.5"},"reference-count":46,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T00:00:00Z","timestamp":1608595200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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-matrices. At non-zero gravitational and string couplings, de Sitter is deformed by corpuscular 1\/N effects, similarly to Witten\u2013Veneziano 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 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.<\/jats:p>","DOI":"10.3390\/sym13010003","type":"journal-article","created":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T20:39:29Z","timestamp":1608669569000},"page":"3","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["S-Matrix and Anomaly of de Sitter"],"prefix":"10.3390","volume":"13","author":[{"given":"Gia","family":"Dvali","sequence":"first","affiliation":[{"name":"Arnold Sommerfeld Center, Ludwig-Maximilians-University, 80333 Munich, Germany"},{"name":"Max-Planck-Institute for Physics, 80805 Munich, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"023","DOI":"10.1088\/1475-7516\/2014\/01\/023","article-title":"Quantum Compositeness of Gravity: Black Holes, AdS and Inflation","volume":"1","author":"Dvali","year":"2014","journal-title":"J. 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