  We investigate the bubble nucleation in five dimensional spacetime catalyzed
by quintessence. We especially focus on decay of a metastable Minkowski vacuum
to an anti-de Sitter vacuum and study dynamics of the bubble on which four
dimensional expanding universe is realized. We also discuss the trans-Planckian
censorship conjecture and impose a constraint on the parameter space of the
catalysis. As an application of this model, we propose an inflation mechanism
and an origin of the dark energy in the context of quintessence in five
dimensions.
