  We examine the behaviour of a closed oscillating universe filled with a
homogeneous scalar field and find that, contrary to naive expectations, such a
universe expands to larger volumes during successive expansion epochs. This
intriguing behaviour introduces an arrow of time in a system which is
time-reversible. The increase in the maximum size of the universe is closely
related to the work done on/by the scalar field during one complete oscillatory
cycle which, in turn, is related to the asymmetry in the scalar field equation
of state during expansion and collapse. Our analysis shows that scalar fields
with polynomial potentials $V(\phi) = \lambda \phi^q$, $q > 1$ lead to a
growing oscillation amplitude for the universe: the increase in amplitude
between successive oscillations is more significant for smaller values of $q$.
Such behaviour allows for the effective recycling of the universe. A recycled
universe can be quite old and can resolve the flatness problem. These results
have strong bearing on cosmological models in which the role of dark matter is
played by a scalar field. They are also relevant for chaotic inflationary
models of the early universe since they demonstrate that, even if the universe
fails to inflate the first time around, it will eventually do so during future
oscillatory cycles. Thus, the space of initial conditions favourable for
chaotic inflation increases significantly.
