Fractal initial conditions and natural parameter values in hybrid inflation

We show that the initial field values required to produce inflation in the two fields original hybrid model, and its supergravity F-term extension, do not suffer from any fine-tuning problem, even when the fields are restricted to be sub-Planckian and for almost all potential parameter values. This is due to the existence of an initial slow-roll violating evolution which has been overlooked so far. Because of the attractor nature of the inflationary valley, these trajectories end up producing enough accelerated expansion of the Universe. By numerically solving the full nonlinear dynamics, we show that the set of such successful initial field values is connected, of dimension 2 and possesses a fractal boundary of infinite length exploring the whole field space. We then perform a Monte-Carlo-Markov-Chain analysis of the whole parameter space consisting of the initial field values, field velocities, and potential parameters. We give the marginalized posterior probability distributions for each of these quantities such that the Universe inflates long enough to solve the usual cosmological problems. Inflation in the original hybrid model and its supergravity version appears to be generic and more probable by starting outside of the inflationary valley. Finally, the implication of our findings in the context of the eternal inflationary scenario are discussed.