The vacuum bubbles in de Sitter background and black hole pair creation

TL;DR

This paper investigates vacuum bubble nucleation and black hole pair creation in de Sitter space, providing numerical solutions, confirming the applicability of Parke's formula for large bubbles, and calculating pair creation rates.

Contribution

It classifies vacuum bubbles in de Sitter space, extends Parke's formula to large bubbles, and analyzes black hole pair creation with explicit rate calculations.

Findings

Parke's formula applies to large true vacuum bubbles.

Nucleation rates for false vacuum bubbles are evaluated.

Black hole pair creation rates are derived based on bubble solutions.

Abstract

We study the possible types of the nucleation of vacuum bubbles. We classify vacuum bubbles in de Sitter background and present some numerical solutions. The thin-wall approximation is employed to obtain the nucleation rate and the radius of vacuum bubbles. With careful analysis we confirm that Parke's formula is also applicable to the large true vacuum bubbles. The nucleation of the false vacuum bubble in de Sitter background is also evaluated. The tunneling process in the potential with degenerate vacua is analyzed as the limiting cases of the large true vacuum bubble and false vacuum bubble. Next, we consider the pair creation of black holes in the background of bubble solutions. We obtain static bubble wall solutions of junction equation with black hole pair. The masses of created black holes are uniquely determined by the cosmological constant and surface tension on the wall. Finally, we obtain the rate of pair creation of black holes.