Analytic solution of a chaotic inflaton

We directly solve the Langevin equation of motion for a scalar field in the slow-roll limit for a λ${\phi }^4$/4 potential. The probability distribution for the inflaton and several moments of the distribution are also calculated. An upper bound to the percentage deviation of the mean of the distribution from the classical value is also derived. For the case of an initially uniform field, non-Gaussian features only appear when the inflaton deviates from the classical value by more than ∼${\lambda }^{\mathrm{-}1/2}$ standard deviations. We also show that in the non-Gaussian regime the slow-roll Langevin equation of motion is no longer adequate.