Extended inflation with induced gravity

We consider a recently proposed extended model of inflation which improves upon the original old inflation scenario by achieving a graceful exit from the false-vacuum phase. In this paper extended inflation is generalized to include a potential V(φ) for the Brans-Dicke-type field φ. We find that whereas a graceful exit can still be had, the inclusion of a potential places constraints on the percolation time scale for exiting the inflationary phase. Additional constraints on V(φ) and the false-vacuum energy density ${\rho }_F$ from density and gravitational-wave perturbations are discussed. For initially small values of φ the false vacuum undergoes power-law inflation, while for initially large values of φ the expansion is exponential. Within true-vacuum regions slow-rolling inflation can occur. As a result, this model generically leads to multiple episodes of inflation. We discuss the significance these multiple episodes of inflation may have on the formation of large-scale structure and the production of voids.