Constraining inflation

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Abstract
We analyze the theoretical limits on slow roll reconstruction, an optimal algorithm for recovering the inflaton potential (assuming a single-field slow roll scenario) from observational data. Slow roll reconstruction is based upon the Hamilton–Jacobi formulation of the inflationary dynamics. 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 the bounds on the slow roll parameters from future data sets. A minimal running of the spectral index, induced solely by the first two slow roll parameters ( and η), appears to be effectively undetectable by realistic cosmic microwave background (CMB) experiments. However, since the ability to detect any running increases with the lever arm in comoving wavenumber, 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.