Ups and downs of cyclic universes

We investigate homogeneous and isotropic oscillating cosmologies with multiple fluid components. Transfer of energy between these fluids is included in order to model the effects of nonequilibrium behavior on closed universes. We find exact solutions which display a range of new behaviors for the expansion scale factor. Detailed examples are studied for the exchange of energy from dust or a scalar field into radiation. We show that, contrary to expectation, it is unlikely that such models can offer a physically viable solution to the flatness problem.

Figure 1

The evolution of the scale factor in a closed universe with radiation and a scalar field exchanging energy, as prescribed in Eq. (15) when $0<s\propto \rho a^{-1}$.

Figure 2

The evolution of the scale factor in a closed universe with radiation and a scalar field exchanging energy, as prescribed in Eq. (16) when $0<s\propto a^{-5}$.

Figure 3

The evolution of the scale factor in a flat universe with radiation and vacuum exchanging energy, as prescribed in Eq. (19) when $0<s\propto \Lambda$.

Figure 4

The evolution of the scale factor in a flat universe with radiation and vacuum exchanging energy, as prescribed in Eq. (20) when $0<s=\mathrm{\text{constant}}$.