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

TL;DR

This paper uses numerical relativity to identify conditions on scalar field potentials that enable robust slow contraction and a graceful exit, emphasizing the importance of potential shape and ultralocality.

Contribution

It demonstrates that negative potentials with specific slope conditions ensure robustness in slow contraction, and that the potential's minimum is crucial for a graceful exit.

Findings

Negative potentials with $M_{Pl}|V_{,\, ext{phi}}/V| extgreater 5$ are essential for robustness.

A potential minimum is necessary for a graceful exit from slow contraction.

Ultralocality is key to both smoothing and exit processes.

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.