Recycling the universe using scalar fields

Abstract

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 vol- umes during successive expansion epochs. This intriguing be- haviour introduces an arrow of time in a system which is time- reversible. The increase in the maximum size of the universe s closely related to the work done on/by the scalar field dur- ng one complete oscillatory cycle which, in turn, is related to the asymmetry in the scalar field equation of state dur- ng expansion and collapse. Our analysis shows that scalar fields with polynomial potentials V (φ) = λφq , q > 1 lead to a growing oscillation amplitude for the universe: the increase n amplitude between successive oscillations is more signifi- cant 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 rele- vant 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 oscil- atory cycles. Thus, the space of initial conditions favourable or chaotic inflation increases significantly.