Generation of non-Gaussian fluctuations during chaotic inflation

We solve the stochastic evolution equations for the inflation field during the slow-roll period of chaotic inflation. We find exact analytic solutions for the V(Φ)=λΦ44 potential. We provide an explicit demonstration of the dependence of the solutions on the interpretation of the random noise. The resulting probability distributions are sharply peaked around the classical deterministic trajectory and are almost Gaussian. The exact probability distributions show that the skewness is very sensitively dependent on λ and also weakly dependent on initial and final conditions. The number of effective standard deviations, N, required for significant non-Gaussian effects is given by N>const×λ-16 where the constant (>10-2) is determined by initial and final conditions. Taking uncertainties in these conditions into account, non-Gaussian effects become important for rare events (N∼8) when λ>∼10-10. However, the current constraint on λ<∼5×10-14 for adiabatic fluctuations makes non-Gaussian effects very small. Improved constraints on λ can completely rule out any significant non-Gaussian effects in inflation-generated adiabatic fluctuations.