Title: "New applications of stochastic inflation"
In the stochastic formulation of inflation, the quantum fluctuations
arising on small scales are collected in a classical noise term that
perturbs the classical evolution on super-Hubble scales. We review the
derivation of the Langevin equation for the long-wavelength modes, and
analyze the statistical properties of its solution in dependence on the
characteristics of the noise.
We provide a calculation of the power spectrum of the cosmological
perturbations in the case of a colored noise, and we show that a blue
tilt on the largest observable scales is found when one properly accounts
for the local homogeneity of our patch of the Universe before the Hubble
crossing (in agreement with the WMAP data showing a suppression of the
low multipoles of the CMB anisotropy).
When self-interaction is introduced, the probability distribution of the
observable fluctuations preserve some memory of the higly non-Gaussian
ultra-large-scale dynamics: as a consequence of the cross talk between
scales induced by colored noise the intrinsic non-Gaussianity is
substantially enhanced also on observable scales.
We finally describe the stochastic evolution of a quintessence field
during inflation. In this case quantum fluctuations drive the
quintessence field out of the range of values allowed by the
observations, unless a constraint on the total amount of inflation is