New type of hill-top inflation

TL;DR

This paper introduces a novel hill-top inflation model based on initial conditions from a microcanonical density matrix, involving cosmological instantons and oscillations, with potential shapes generated by quantum corrections in specific gravity models.

Contribution

It proposes a new hill-top inflation scenario derived from initial conditions set by cosmological instantons and explores its realization in non-minimal Higgs inflation and $R^2$-gravity models.

Findings

Initial conditions from microcanonical density matrix lead to hill-top inflation.

Oscillatory instanton solutions describe underbarrier inflaton dynamics.

Logarithmic loop corrections shape the inflaton potential.

Abstract

We suggest a new type of hill-top inflation originating from the initial conditions in the form of the microcanonical density matrix for the cosmological model with a large number of quantum fields conformally coupled to gravity. Initial conditions for inflation are set up by cosmological instantons describing underbarrier oscillations in the vicinity of the inflaton potential maximum. These periodic oscillations of the inflaton field and cosmological scale factor are obtained within the approximation of two coupled oscillators subject to the slow roll regime in the Euclidean time. This regime is characterized by rapid oscillations of the scale factor on the background of a slowly varying inflaton, which guarantees smallness of slow roll parameters $\epsilon$ and $\eta$ of the following inflation stage. A hill-like shape of the inflaton potential is shown to be generated by logarithmic loop corrections to the tree-level asymptotically shift-invariant potential in the non-minimal Higgs inflation model and $R^2$-gravity. The solution to the problem of hierarchy between the Planckian scale and the inflation scale is discussed within the concept of conformal higher spin fields, which also suggests the mechanism bringing the model below the gravitational cutoff and, thus, protecting it from large graviton loop corrections.