\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We study the false vacuum decay and bubble nucleation in the presence of a cosmic string in de Sitter spacetime. A cosmic string induces a deficit angle in spacetime around itself so the nucleated bubble has the shape of a rugby ball. Working in thin wall approximation and using the junction conditions we study the dynamics of the bubble wall and calculate the Euclidean action. An interesting feature in our analysis is that the tension of the string is screened by the bubble such that an observer inside the bubble measures a different value of the tension than an outside observer. We show that the string can act as a catalyzer in which the nucleation rate is enhanced compared to the ColemanÃ¢??de Luccia instanton. However, in general, the nucleation rate is not a monotonic function of the difference between the two tensions so in some regions of the parameters space the nucleation rate may be smaller than the ColemanÃ¢??de Luccia bubble
\end{document}