Why concave rather than convex inflaton potential?

Pisin Chen,Dong-Han Yeom

doi:10.1140/epjc/s10052-018-6357-0

Abstract

The Planck data on cosmic microwave background indicates that the Starobinsky-type model with concave inflation potential is favored over the convex-type chaotic inflation. Is there any reason for that? Here we argue that if our universe began with a Euclidean wormhole, then the Starobinsky-type inflation is probabilistically favored. It is known that for a more generic choice of parameters than that originally assumed by Hartle and Hawking, the Hartle–Hawking wave function is dominated by Euclidean wormholes, which can be interpreted as the creation of two classical universes from nothing. We show that only one end of the wormhole can be classicalized for a convex potential, while both ends can be classicalized for a concave potential. The latter is therefore more probable.

Highlights

How did the universe begin? This has long been one of the most fundamental questions in physics
The Big Bang scenario, when tracing back to the Planck time, indicates that the universe should start from a regime of quantum gravity [1] that is describable by a wave function of the universe governed by the Wheeler-DeWitt (WDW) equation [2]
We investigate Euclidean wormholes in the context of the inflationary scenario in order to answer the question on the preference of a specific shape of the inflaton potential

Summary

Introduction

How did the universe begin? This has long been one of the most fundamental questions in physics. If the arrow of time is symmetric between positive and negative time for classical histories, one may interpret this situation as having two universes created from nothing, where the probability is determined by the instanton that connects the two classical universes [12].1 Such a process can be well described by the Euclidean wormholes2 [13,14,15,16,17] (see [18,19,20]). If the inflaton field is constant and the potential is flat (V (φ) = V0), we recover the original Hartle–Hawking no-boundary scenario In such case the scale factor should satisfy a 2 + Veff (a) = 0,. Since Veff < 0 is the allowed region for the Euclidean signature, this describes a compact instanton

Why Euclidean wormholes?

Inflaton potentials and initial conditions

Preference of concave inflaton potential

Discussion