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We consider constraints on inflation driven by a single, minimally coupledscalar field in the light of the WMAP5 dataset, as well as ACBAR and theSuperNova Legacy Survey. We use the Slow Roll Reconstruction algorithm toderive optimal constraints on the inflationary parameter space. The scaledependence in the slope of the scalar spectrum permitted by WMAP5 is largeenough to lead to viable models where the small scale perturbations have asubstantial amplitude when extrapolated to the end of inflation. We find thatexcluding parameter values which would cause the overproduction of primordialblack holes or even the onset of eternal inflation leads to potentiallysignificant constraints on the slow roll parameters. Finally, we present a moresophisticated approach to including priors based on the total duration ofinflation, and discuss the resulting restrictions on the inflationary parameterspace.

Primordial Black Holes, Eternal Inflation, and the Inflationary Parameter Space after WMAP5