Recycling the universe using scalar fields

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.