Primordial black holes, eternal inflation, and the inflationary parameter space after WMAP5

We consider constraints on inflation driven by a single, minimally coupled scalar field in the light of the WMAP5 (WMAP: Wilkinson Microwave Anisotropy Probe) data set, as well as ACBAR (Arcminute Cosmology Bolometer Array Receiver) and the SuperNova Legacy Survey. We use the slow roll reconstruction algorithm to derive optimal constraints on the inflationary parameter space. The scale dependence in the slope of the scalar spectrum permitted by WMAP5 is large enough to lead to viable models where the small scale perturbations have a substantial amplitude when extrapolated to the end of inflation. We find that excluding parameter values which would cause the overproduction of primordial black holes or even the onset of eternal inflation leads to potentially significant constraints on the slow roll parameters. Finally, we present a more sophisticated approach to including priors based on the total duration of inflation, and discuss the resulting restrictions on the inflationary parameter space.