  Slow roll reconstruction is derived from the Hamilton-Jacobi formulation of
inflationary dynamics. It automatically includes information from sub-leading
terms in slow roll, and facilitatesthe inclusion of priors based on the
duration on inflation. We show that at low inflationary scales the
Hamilton-Jacobi equations simplify considerably. We provide a new
classification scheme for inflationary models, based solely on the number of
parameters needed to specify the potential, and provide forecasts for likely
bounds on the slow roll parameters from future datasets. A minimal running of
the spectral index, induced solely by the first two slow roll parameters
(\epsilon and \eta) appears to be effectively undetectable by realistic Cosmic
Microwave Background experiments. However, we show that the ability to detect
this signal increases with the lever arm in comoving wavenumber, and we
conjecture that high redshift 21 cm data may allow tests of second order
consistency conditions on inflation. Finally, we point out that the second
order corrections to the spectral index are correlated with the inflationary
scale, and thus the amplitude of the CMB B-mode.

Astrophysics