Stochastic growth of vector field condensates during inflation
Bueno Sanchez, Juan Carlos (Universidad Complutense de Madrid)

In recent years, vector fields have been shown to be capable of generating a nearly scale-invariant spectrum of the curvature perturbation, hence alleviating the need to find fundamental scalar fields to fulfill the task. When generated by vector fields, the primordial curvature perturbation possesses observationally interesting features like statistical anisotropy and non-gaussianity, whose magnitude is determined by the expectation value of the quasi-homogeneous vector field produced during inflation. I study the stochastic growth of vector fields in the context of some supergravity theories using the Fokker-Planck approach to compute the typical magnitude of the vector condensate and its probability distribution function. Remarkably, and unlike the stochastic growth of scalar field condensates during inflation, the vector condensate obtains its expectation values according to an out-of equilibrum distribution function which remains frozen after a few e-foldings of inflation. The implications of this result for the statistical anisotropy and non-gaussianity generated by the vector field are discussed.