In order to draw out the essential behavior of the universe, investigations
of early universe cosmology often reduce the complex system to a simple
integrable system. Inflationary models are of this kind as they focus on simple
scalar field scenarios with correspondingly simple dynamics. However, we can be
assured that the universe is crowded with many interacting fields of which the
inflaton is but one. As we describe, the nonlinear nature of these interactions
can result in a complex, chaotic evolution of the universe. Here we illustrate
how chaotic effects can arise even in basic models such as homogeneous,
isotropic universes with two scalar fields. We find inflating universes which
act as attractors in the space of initial conditions. These universes display
chaotic transients in their early evolution. The chaotic character is reflected
by the fractal border to the basin of attraction. The broader implications are
likely to be felt in the process of reheating as well as in the nature of the
cosmic background radiation.Comment: 16 pages, RevTeX. See published version for fig