Simulating first-order phase transition during inflation

Ending the inflation by vacuum decay is considered infeasible due to the graceful-exit problem. Even if considering an alternative field other than the inflaton to realize a first-order phase transition (FoPT) during inflation, it is usually challenging in concrete model building, as bubble nucleations might not be fast and dense enough to successfully end inflation. In this work, we propose a FoPT at the grand-unification-theory (GUT) scale within the Starobinsky inflation. The key construction is an exponentially evolving potential barrier dynamically controlled by the rolling inflaton, so that almost no bubbles nucleate during the early inflationary era, but with a large number of bubbles nucleating near the end of inflation. With lattice numerical simulations, we have successfully tested this GUT-FoPT during Starobinsky inflation, and the resulting gravitational-wave energy density spectrum reproduces previous analytical estimation with a distinctive oscillation feature at high frequencies.