INFLATIONARY STOCHASTIC DYNAMICS AND THE STATISTICS OF LARGE-SCALE STRUCTURE

We examine the nonlinear multiplicative stochastic behavior of chaotic inflation with an emphasis on possible non-Gaussian statistics in ini tial conditions for cosmological large-scale structure formation. Larg e-scale mode-mode couplings are analyzed using stochastic dynamics. We reach the following conclusions: 1. Coarse-grained (long-wavelength) scalar fields become nonlinear stochastic variables whose evolution sh ows behavior unexpected in the classical analysis. The interplay betwe en the classical roll-down (drift) and quantum mechanical fluctuations (diffusion) makes the evolution of the scalar fields extremely noncla ssical. Only during the very late stages of chaotic inflation do the s calar fields acquire their classical interpretation (i.e., as determin istic variables). 2. The statistics of initial conditions for cosmolog ical density fluctuations depend on the details of scalar field dynami cs during inflation. A non-Gaussian distribution of density fluctuatio ns is a generic feature in chaotic inflation models. However, the astr ophysical importance of this effect is strongly model dependent. Gener ally, deviations from Gaussian statistics are dependent on the strengt h of the nonlinear self-interaction of the scalar fields. Adiabatic fl uctuations were expected to show significant non-Gaussian effects in s ingle shot inflation only on superhorizon scales due to the strong con straint imposed by the cosmic microwave background radiation anisotrop y limit. This conclusion is valid for a wide range of models. 3. In a simple chaotic double inflation model, non-Gaussian effects can be ast rophysically significant, especially on very large scales. In this mod el, non-Gaussian statistics can be weakly scale dependent. Non-Gaussia n effects could be observable on large scales at a level of approximat ely a few standard deviations. We also find that some chaotic potentia ls, designed to give non-scale-invariant density fluctuations, result in strong non-Gaussian phase correlations. 4. In multiple field models , non-Gaussian effects can be important. This depends on the nature of the secondary fields (massive or massless). Multiple field dynamics c an provide non-Gaussian statistics as well as nonflat (scale-dependent ) spectra. We point out that initial conditions for the large-scale st ructure in inflationary scenarios in the simplest models are Gaussian to a very high precision. However, as we are forced to consider more f inely tuned models of inflation, Gaussian initial conditions should no t be taken for granted, even on astrophysically interesting (i.e., obs ervable) scales.