Stochastic stage of an inflationary universe model

Using the stochastic description of a scalar field on its phase space, we analyse the early stage of a new inflationary universe model with a Higgs-type potential. At this stage, quantum fluctuations play an important role for the dynamics of the scalar field as well as the classical potential force. We find that the velocity dispersion of the field 〈 φ{symbol} ̇²〉 becomes negligible within the Hubble timescale and the slow roll-over phase is realized, provided that 〈 φ{symbol} ̇²〉≲〈V(φ{symbol})〉 and λ〈φ{symbol}²〉 ²≪〈V(φ{symbol})〉 initially, where λ is the quartic coupling constant. This supports the picture that inflation can set in for a wide class of pre-inflationary states, including thermal states, and the behavior of the scalar fields is independent of such states. It also verifies the use of the slow roll-over approximation for most states of inflation.