"Graceful" Old Inflation
  We show that Inflation in a False Vacuum becomes viable in the presence of a spectator scalar field non minimally coupled to gravity. The field is unstable in this background, it grows exponentially and slows down the pure de Sitter phase itself, allowing then fast tunneling to a true vacuum. We compute the constraint from graceful exit through bubble nucleation and the spectrum of cosmological perturbations. 
Fabrizio Di Marco, Alessio Notari