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. Due to the attractor nature of the inflationary valley, these
trajectories end up producing enough accelerated expansion of the universe. By
numerically solving the full non-linear dynamics, we show that the set of such
successful initial field values is connected, of dimension two 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 marginalised 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.
