Latest inflation model constraints from cosmic microwave background measurements: Addendum

We present an update of cosmological constraints on single-field inflation in light of the Wilkinson Microwave Ansiotropy Probe satellite mission five-year results (WMAP5). We find that the cosmic microwave background data are quite consistent with a Harrison-Zel'dovich primordial spectrum with no running and zero tensor amplitude. We find that the three main conclusions of our analysis of the WMAP three-year data (WMAP3) are consistent with the WMAP5 data: (1) the Harrison--Zel'dovich model is within the 95% confidence level contours; (2) there is no evidence for running of the spectral index of scalar perturbations; (3) From the WMAP 5 data alone, potentials of the form $V \propto \phi^p$ are consistent with the data for $p = 2$, and are ruled out for $p = 4$. Furthermore, consistent with our WMAP3 analysis, we find no evidence for primordial tensor perturbations, this time with a 95% confidence upper limit of $r < 0.4$ for the WMAP5 data alone, and $r < 0.35$ for the WMAP5 data taken in combination with the Arcminute Cosmology Bolometer Array (ACBAR).