Inflation and the Scale Dependent Spectral Index: Prospects and
  Strategies
  We consider the running of the spectral index as a probe of both inflation
itself, and of the overall evolution of the very early universe. Surveying a
collection of simple single field inflationary models, we confirm that the
magnitude of the running is relatively consistent, unlike the tensor amplitude,
which varies by orders of magnitude. Given this target, we confirm that the
running is potentially detectable by future large scale structure or 21 cm
observations, but that only the most futuristic measurements can distinguish
between these models on the basis of their running. For any specified
inflationary scenario, the combination of the running index and unknown
post-inflationary expansion history induces a theoretical uncertainty in the
predicted value of the spectral index. This effect can easily dominate the
statistical uncertainty with which Planck and its successors are expected to
measure the spectral index. More positively, upcoming cosmological experiments
thus provide an intriguing probe of physics between TeV and GUT scales by
constraining the reheating history associated with any specified inflationary
model, opening a window into the "primordial dark age" that follows the end of
inflation.
