We discuss a new concept of cosmological initial conditions in the form of the microcanonical density matrix and apply it to the cosmological model driven by a large number of conformal fields. This model features dynamical restriction of the cosmological constant range and, thus, might serve as a solution of the string landscape problem. In particular, it suggests a new mechanism of hill-top inflation originating from the underbarrier field oscillations in the vicinity of the inflaton potential maxima. Applications of this mechanism to Higgs inflation and Starobinsky models are considered. The problem of hierarchy between the inflation and Planck scales is discussed within the concept of a hidden sector of conformal fields with arbitrarily high spins. Thermal corrections to the primordial power spectrum and other properties of this model are briefly discussed.
