Strong-coupling scale and frame-dependence of the initial conditions for
  chaotic inflation in models with modified (coupling to) gravity
  A classical evolution in chaotic inflationary models starts at high energy
densities with semi-classical initial conditions presumably consistent with
universal quantum nature of all the fundamental forces. That is each quantum
contributes the same amount to the energy density. We point out the upper limit
on this amount inherent in this approach, so that all the quanta are inside the
weak-coupling domain. We discuss this issue in realistic models with modified
gravity, $R^2$- and Higgs-inflations, emphasizing the specific change of the
initial conditions with metric frame, while all the quanta still contribute
equal parts. The analysis can be performed straightforwardly in any model with
modified gravity ($F(R)$-gravity, scalars with non-minimal couplings to
gravity, etc).
