Starobinsky has suggested an inflationary cosmological scenario in which the inflation is driven by quantum corrections to the vacuum Einstein’s equations. Here a detailed review of the Starobinsky scenario is given and an observational constraint on the parameters of the model is derived. The quantum mechanics of the model is studied first using the instanton method, and then by solving the corresponding Wheeler-DeWitt equation. A cosmological wave function is obtained describing a universe tunneling from ‘‘nothing’’ to the Starobinsky inflationary phase. The curvature fluctuations in the tunneling universe are calculated. This quantum analysis determines the initial conditions for the classical evolution of the model.

• Received 19 April 1985

DOI:https://doi.org/10.1103/PhysRevD.32.2511