New type of hill-top inflation

A.O Barvinsky,D.V Nesterov,A.Yu Kamenshchik

doi:10.1088/1475-7516/2016/01/036

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 ϵ and η 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 R2-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.

Highlights

Once very popular the problem of initial conditions in cosmology [1, 2] starts attracting attention again
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
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 suggests the mechanism bringing the model below the gravitational cutoff and, protecting it from large graviton loop corrections

Summary

Introduction

Once very popular the problem of initial conditions in cosmology [1, 2] starts attracting attention again. The model that circumvents the above problems and is based on first principles of canonical quantization was suggested in [16, 17] It represents the synthesis of two main ideas – a new concept of the cosmological microcanonical density matrix as the initial state of the Universe and application of this concept to the system with a large number of quantum fields conformally coupled to gravity. The qualitative picture of the hill-top inflation is shown on Fig.1 – the inflaton slowly rolling from the potential hill in real Lorentzian time originates from its underbarrier oscillations after the Euclidean-Lorentzian transition at the turning point φ∗ This is, not a tunneling in the usual sense, because there is no classically allowed state before this tunneling, and the cosmological instanton in the underbarrier regime is just the saddle point of the microcanonical partition function

The model with the fundamental cosmological constant

Dynamical inflaton in conformal cosmology

The shape of the potential: non-minimal Higgs inflation and R2 model

Conclusions