  We begin by enumerating the many processes in gravitation and cosmology where
quantum noise and fluctuations play an active role such as particle creation,
galaxy formation and entropy generation. Using the influence functional we
first explain the origin and nature of noise in quantum systems interacting
with an environment at a finite temperature. With linear coupling to nonohmic
baths or at low temperatures, colored noise and nonlocal dissipation would
appear and for nonlinear coupling multiplicative noise is generally expected.
We derive a generalized fluctuation- dissipation relation for these systems.
Then using a model of quantum Brownian motion in a bath of parametric
oscillators, we show how noise and dissipation can be related to the Bogolubov
coefficients of parametric amplification, which in the second-quantized sense,
depicts cosmological particle creation in a dynamic background. We then
calculate the influence functional and study the noise characteristics of
quantum fields as probed by a particle detector. As examples, we show that an
uniformly- accelerated observer in flat space or an inertial observer in an
exponentially expanding (de Sitter) universe would see a thermal particle
spectrum, recovering the well-known results of Unruh and Gibbons and Hawking ,
as inspired by the Hawking effect in black holes. We show how this method can
be effectively used for treating the backreaction of particle creation and
other quantum field processes on the
