  We study the dynamics of homogeneous, isotropic universes which are governed
by the Eddington-inspired alternative theory of gravity which has a single
extra parameter, $\kappa$. Previous results showing singularity-avoiding
behaviour for $\kappa > 0$ are found to be upheld in the case of domination by
a perfect fluid with equation of state parameter $w > 0$. The range $-1/3 < w <
0$ is found to lead to universes which experience unbounded expansion rate
whilst still at a finite density. In the case $\kappa < 0$ the addition of
spatial curvature is shown to lead to the possibility of oscillation between
two finite densities. Domination by a scalar field with an exponential
potential is found to also lead to singularity-avoiding behaviour when $\kappa
> 0$. Certain values of the parameters governing the potential lead to
behaviour in which the expansion rate of the universe changes sign several
times before transitioning to regular GR-like behaviour.
