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Abstract

We use numerical relativity simulations to explore the conditions for a
canonical scalar field $\phi$ minimally coupled to Einstein gravity to generate
an extended phase of slow contraction that robustly smooths the universe for a
wide range of initial conditions and then sets the conditions for a graceful
exit stage. We show that to achieve robustness it suffices that the potential
$V(\phi)$ is negative and $M_{\rm Pl}|V_{,\phi}/V|\gtrsim5$ during the
smoothing phase. We also show that, to exit slow contraction, the potential
must have a minimum. Beyond the minimum, we find no constraint on the uphill
slope including the possibility of ending on a positive potential plateau or a
local minimum with $V_{\rm min}>0$. Our study establishes ultralocality for a
wide range of potentials as a key both to robust smoothing and to graceful
exit.