Study of the Coleman - de Luccia instanton of the second order

TL;DR

This paper investigates the second order Coleman-de Luccia instanton, deriving an approximate formula through perturbative expansion and performing numerical analysis for specific potentials.

Contribution

It introduces a perturbative method to approximate the second order instanton and provides numerical results for quasi-exponential potentials.

Findings

Derived an approximate formula for the instanton using perturbation theory.

Numerically analyzed the instanton in quasi-exponential potential scenarios.

Identified conditions under which the second order instanton appears.

Abstract

We study the second order Coleman - de Luccia instanton which appears as the curvature of the effective potential reaches a sufficiently large value. We show how one can find the approximative formula for this instanton by perturbative expansion in the case when the second derivative of the effective potential divided by the Hubble parameter squared is close to -10, and we perform a numerical study of this instanton in the case of quasi-exponential potential.