# Why concave rather than convex inflaton potential?

## TL;DR

This paper explains why a concave inflaton potential is favored in the universe's early moments, linking it to the probability of classicalization in Euclidean wormhole scenarios, aligning with observational data.

## Contribution

It demonstrates that Euclidean wormholes favor concave potentials over convex ones by analyzing classicalization conditions, providing a theoretical reason for observational preferences.

## Key findings

- Concave potentials allow both ends of a wormhole to classicalize.
- Convex potentials restrict classicalization to only one end.
- The probabilistic analysis favors concave inflaton potentials.

## 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.