The robustness of slow contraction and the shape of the scalar field potential

Abstract

We use numerical relativity simulations to explore the conditions for a canonical scalar field ϕ 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(ϕ) is negative and M Pl|V, ϕ /V|≳5 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 min > 0.Our study establishes ultralocality, i.e., all spatial gradients quickly becoming negligible, for a wide range of potentials as a key both to robust smoothing and to graceful exit.