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-matrices. 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 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.
Highlights
In classical General Relativity (GR), the de Sitter metric is sourced by a positive vacuum energy density, Λ, which we call cosmological constant
To get a would-be de Sitter vacuum in ten dimensions, we must take the ten-dimensional Newton constant G(10) to zero while keeping R−dS2 = ΛG(10) finite. In such a limit, the string coupling, gs2 = Ms8G(10), vanishes for any finite value of the string scale Ms as in pure gravity, in full string theory, even a hypothetical existence of de Sitter vacuum is incompatible with the closed string scattering
The above simple argument encodes a profound point. It shows that a cosmological background can serve as an eternal de Sitter vacuum but only at the expense of trivializing quantum gravity
Summary
In classical General Relativity (GR), the de Sitter metric is sourced by a positive vacuum energy density, Λ, which we call cosmological constant (or a cosmological term). This parameter is highly sensitive to a cutoff of the theory. For non-zero values of gs and G (finite N), the system must exit gracefully from the de Sitter state before the time tQ elapses This imposes a general constraint that a cosmological source must evolve faster than the quantum break-time. In this way, thanks to its S-matrix formulation, string theory nullifies an outstanding cosmological puzzle.
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