Analysis of inflation driven by a scalar field and a curvature-squared term

The evolution of an isotropic cosmological model in the R+${\mathit{R}}^2$ theory of gravity with a coherent massive scalar field is studied analytically and numerically. For certain initial conditions, the model goes through a superinflationary stage (Ḣ>0) followed by usual subinflation (Ḣ<0). Double inflation consisting of two inflationary stages divided by a period of power-law expansion a(t)∝${\mathit{t}}^{2/3}$ is possible if the scalar particle mass is small compared to the mass of the scalaron (scalar graviton). The spectrum of adiabatic perturbations generated from vacuum quantum fluctuations is investigated. It is quasiflat (though not necessarily varying monotonically with scale) in the case of single inflation; for double inflation, it has a characteristic step.