In an induced-gravity model, the stability condition of an inflationary slow-rollover solution is shown to be ${\phi }_0{\partial }_{{\phi }_0}V\left({\phi }_0\right)=4V\left({\phi }_0\right).\mathrm{}$ The presence of higher derivative terms will, however, act against the stability of this expanding solution unless further constraints on the field parameters are imposed. We find that these models will acquire a nonvanishing cosmological constant at the end of inflation. Some models are analyzed for their implication to the early universe.

• Received 23 March 2000

DOI:https://doi.org/10.1103/PhysRevD.62.087301