  We investigate cosmological models described by a scalar field with an
exponential potential, and apply the stochastic formalism, which allows us to
study how quantum field fluctuations give rise to stochastic noise. This
modifies the classical dynamics of the scalar field at large scales, above a
coarse-graining scale. In particular we explore how quantum field fluctuations
perturb the equation of state on large scales which can lead to a quantum
instability of the classical collapse solution below the Planck scale in the
case of a pressureless collapse.
