One-loop bosonic string and De Sitter space

TL;DR

This paper computes one-loop string amplitudes to derive an effective action that admits small-curvature de Sitter solutions, suggesting a possible string-theoretic origin of accelerated expansion.

Contribution

It provides the first explicit derivation of a low-energy effective action from one-loop bosonic string amplitudes that supports de Sitter solutions.

Findings

Effective action admits weakly-curved de Sitter solutions.

One-loop couplings comparable to tree-level in supercritical dimensions.

Higher-loop corrections are negligible in the considered regime.

Abstract

We calculate the bosonic string one-loop three- and four-point amplitudes to quadradic order in momentum, and we read off the one-loop low-energy two-derivative effective action for the massless fields, $S_{eff}$. Treating the renormalized one-loop vacuum energy as a tunable parameter and extrapolating to a supercritical dimension $D > 26$, one can reach a regime where the one-loop couplings in Seff are of the same order as the tree-level ones while all higher-loop corrections are negligible. Moreover the effective spacetime curvature is small in string units. We show that the effective action thus obtained admits weakly-curved de Sitter solutions with constant dilaton at small string coupling.