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 $\varphi$ 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 $V(\varphi )$ is negative and $M_{\mathrm{Pl}}|V_{,\varphi }/V|\gtrsim 5$ 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 for a wide range of potentials as a key both to robust smoothing and to graceful exit.

23 pages, 7 figures

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Cited by in corpus (1)

• Negative scalar potentials and the swampland: an Anti-Trans-Planckian Censorship Conjecture