Anamorphosis in hybrid inflation: How to avoid fine-tuning of initial conditions?

In order to generate more than 60 e-folds of accelerated expansion in original hybrid inflation, 2-fields trajectories are usually required to be initially fine-tuned in a very narrow band along the inflationary valley or in some isolated points outside it. From a more precise investigation of the dynamics, these points which can cover a non-negligible proportion of the space of sub-planckian initial field values, depending on the potential parameters, are shown to be organised in connected domains with fractal boundaries. They correspond to trajectories first falling towards the bottom of the potential, then climbing and slow-rolling back along the inflationary valley. The full parameter space, including initial velocities and all the potential parameters, is then explored by using Monte-Carlo-Markov-Chains (MCMC) methods. Results indicate that successful initial conditions (IC) outside the valley are not localized in the parameter space and are the dominant way to realise inflation, independently of initial field velocities. Natural bounds on parameters are deduced. The genericity of our results is confirmed in 5 other hybrid models from various framework.