Cosmic Perturbations from a Rotating Field

Complex scalar fields charged under approximate $U(1)$ symmetries appear in well-motivated extensions of the Standard Model. One example is the field that contains the QCD axion field associated with the Peccei-Quinn symmetry; others include flat directions in supersymmetric theories with baryon, lepton, or flavor charges. These fields may take on large values and rotate in field space in the early universe. The relevant approximate $U(1)$ symmetry ensures that the angular direction of the complex field is light during inflation and that the rotation is thermodynamically stable and is long-lived. These properties allow rotating complex scalar fields to naturally serve as curvatons and explain the observed perturbations of the universe. The scenario imprints non-Gaussianity in the curvature perturbations, likely at a level detectable in future large scale structure observations. The rotation can also explain the baryon asymmetry of the universe without producing excessive isocurvature perturbations.