Next-generation test of cosmic inflation

The increasing precision of cosmological datasets is opening up new opportunities to test predictions from cosmic inflation. Here we study the impact of high precision constraints on the primordial power spectrum and show how a new generation of observations can provide impressive new tests of the slow-roll inflation paradigm, as well as produce significant discriminating power among different slow-roll models. In particular, we consider next-generation measurements of the Cosmic Microwave Background (CMB) temperature anisotropies and (especially) polarization, as well as new Lyman-$\alpha$ measurements that could become practical in the near future. We emphasize relationships between the slope of the power spectrum and its first derivative that are nearly universal among existing slow-roll inflationary models, and show how these relationships can be tested on several scales with new observations. Among other things, our results give additional motivation for an all-out effort to measure CMB polarization.Comment: 10 pages, 8 figures, to appear in PRD; major changes are a reanalysis in terms of better cosmological parameters and clarifications on the contributions of polarization and Lyman-alpha dat