Axions and inflation: String formation during inflation

The Peccei-Quinn field ψ=re^iθ√2 has a Mexican hat potential 1/4λ(r²-fₐ²)², and the axion, with the field fₐθ, is its Nambu-Goldstone boson. During inflation there is a quantum fluctuation in both the radial component r and in the angle θ. If the temperature after inflation is less than fₐ the fluctuation survives, and may be cosmologically significant. Previous investigations of this "inflationary scenario" assumed that r sits in the vacuum, leaving only the angular fluctuation. Here both fluctuations are kept, using the Langevin and Fokker-Planck equations. It is found that for fₐ in the usually accepted range fₐ10¹³ GeV, the radial fluctuation is typically big enough to take ψ over the top of the potential. In that case, strings are produced, which invalidate previous treatments of the inflationary scenario.