  We present non-perturbative numerical relativity simulations of slowly
contracting spacetimes in which the scalar field driving slow contraction is
coupled to a second scalar field through an exponential non-linear sigma
model-type kinetic interaction. These models are important because they can
generate a nearly scale-invariant spectrum of super-Hubble density fluctuations
fully consistent with cosmic microwave background observations. We show that
the non-linear evolution rapidly approaches a homogeneous, isotropic and flat
Friedmann- Robertson-Walker (FRW) geometry for a wide range of inhomogeneous
and anisotropic initial conditions. Ultimately, we find, the kinetic coupling
causes the evolution to deflect away from flat FRW and towards a novel
Kasner-like stationary point, but in general this occurs on time scales that
are too long to be observationally relevant.
