AXIONS AND INFLATION - STRING FORMATION DURING INFLATION

Abstract

The Peccei-Quinn field psi = re(i-theta)/square root 2 has a Mexican hat potential 1/4-lambda(r2-f(a)2)2, and the axion, with the field f(a)theta, is its Nambu-Goldstone boson. During inflation there is a quantum fluctuation in both the radial component r and in the angle 0. If the temperature after inflation is less than f(a), 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 f(a) in the usually accepted range f(a) less than or similar to 10(13) GeV, the radial fluctuation is typically big enough to take psi over the top of the potential. In that case, strings are produced, which invalidate previous treatments of the inflationary scenario.