Abstract
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.