THE CURVATURE PERTURBATION IN POWER LAW (EG EXTENDED) INFLATION

The inflationary contribution to the large scale curvature perturbation is calculated precisely in power law inflation, as well as the resulting constraint on the inflationary potential coming from the observational bound on the microwave background anisotropy. The result is essentially the same as that of earlier approximate calculations; for a scale factor with time dependence a is-proportional-to t(p), the upper bound on the energy scale at the end of inflation decreases exponentially with the p, being equal to 10(14) GeV at p = 6 and to 1O(3) GeV at p = 1.6. In extended inflation these values of p correspond to the Brans-Dicke parameter omega = 10 and omega =