  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.

Astrophysics