  We address two basic issues in the theory of galaxy formation from
fluctuations of quantum fields: 1) the nature and origin of noise and
fluctuations and 2) the conditions for using a classical stochastic equation
for their description. On the first issue, we derive the influence functional
for a $\lambda \phi^4 $ field in a zero-temperature bath in de Sitter universe
and obtain the correlator for the colored noises of vacuum fluctuations. This
exemplifies a new mechanism we propose for colored noise generation which can
act as seeds for galaxy formation with non-Gaussian distributions. For the
second issue, we present a (functional) master equation for the inflaton field
in de Sitter universe. By examining the form of the noise kernel we study the
decoherence of the long-wavelength sector and the conditions for it to behave
classically.
