  We consider a quantum mechanical system to model the effect of quantum fields
on the evolution of the early universe. The system consists of an inverted
oscillator bilinearly coupled to a set of harmonic oscillators. We point out
that the role of noise may be crucial in the dynamics of the oscillator, which
is analyzed using the theory of harmonic oscillators with random frequency.
Using this analogy we argue that, due to the fluctuations around its mean
value, a positive vacuum energy density would not produce an exponentially
expanding but an oscillating universe, in the same fashion that an inverted
pendulum is stabilized by random oscillations of the suspension point
(stochastic Kapitza pendulum). The results emphasize the relevance of noise in
the evolution of the scale factor.
