False vacuum decay with gravity in a critical case

TL;DR

This paper investigates false vacuum decay in a de Sitter universe considering gravitational effects, focusing on potentials near a critical curvature, and compares different instanton solutions to determine decay modes.

Contribution

It introduces an analysis of vacuum decay modes near a critical curvature in the potential, including cases where the fourth derivative is below a critical value.

Findings

Identifies conditions under which Hawking-Moss or Coleman-de Luccia instantons dominate.

Analyzes the impact of potential curvature near a critical value on decay pathways.

Provides insights into vacuum stability in early universe cosmology.

Abstract

The vacuum decay in a de Sitter universe is studied within semiclassical approximation for the class of effective inflaton potentials whose curvature at the top is close to a critical value. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined. The case when the fourth derivative of the effective potential at its top is less than a critical value is discussed.