Are $R^2$- and Higgs-inflations really unlikely?
  We address the question of unlikeness of $R^2$- and Higgs inflations exhibiting exponentially flat potentials and hence apparently violating the inherent in a chaotic inflation initial condition when kinetic, gradient and potential terms are all of order one in Planck units. Placing the initial conditions in the Jourdan frame we find both models not worse than any other models with unbounded from above potentials: the terms in the Einstein frame are all of the same order, though appropriately smaller. 
D.S. Gorbunov and A.G. Panin
astro-ph.CO gr-qc hep-ph