Fate of the false vacuum in string-inspired nonlocal field theory

In this article, we study Coleman bounce in weakly nonlocal theories which are motivated from string field theory. The kinetic term is extended via an infinite series of high-order derivatives, which comes into play at an energy scale $M$, without introducing any new states or ghosts in the mass spectrum. We calculate the bubble nucleation in thin-wall approximation, treating the system in semi-classical manner. We find that the effect of nonlocal scale $M$ in the theory is to suppress the vacuum tunneling rate from false to true vacuum compared to the standard local bouncing scenario. Likewise, we show that as we move further away from the bubble wall, the effects of nonlocality gets reduced and this suppression is significant only around the wall of the nucleated bubble. From our investigations, we conclude that the main effect is due to the fact that the nonlocality smears the solution of the local bubble profile. However, the energy of the bubble wall remains unaffected by the microscopic nonlocal behavior of the theory in the thin-wall approximation. We also discuss the cases for Lee-Wick theories and applications of our result to cosmology.