Origin of inflation in CFT driven cosmology: R2 -gravity and non-minimally coupled inflaton models

We present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology S^1 imes S^3, which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial S^3-section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in R^2 gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters epsilon and eta