On the Generation of Non-Gaussian Fluctuations During Chaotic Inflation

We solve the stochastic evolution equations for the inflaton field during the slow-roll period of chaotic inflation. We find exact analytic solutions for the V(Φ) = λΦ4 /4 potential. The resulting probability distributions are sharply peaked around the classical deterministic trajectory and are approximately gaussian, but the exact probability distributions show that skewness is very sensitively dependent on λ and also weakly dependent on initial and final conditions. The non-Gaussian statistics induced by the nonlinear stochasticity effectively measures the expected level of non-Gaussian deviation in the inflation-generated density fluctuations.