Constraining inflation

Abstract

We analyze the theoretical limits on slow roll reconstruction, an optimal algorithm forrecovering the inflaton potential (assuming a single-field slow roll scenario) fromobservational data. Slow roll reconstruction is based upon the Hamilton–Jacobi formulationof the inflationary dynamics. We show that at low inflationary scales the Hamilton–Jacobiequations simplify considerably. We provide a new classification scheme for inflationarymodels, based solely on the number of parameters needed to specify the potential, andprovide forecasts for the bounds on the slow roll parameters from future data sets. Aminimal running of the spectral index, induced solely by the first two slow roll parameters(ϵ and η), appears to be effectively undetectable by realistic cosmic microwave background(CMB) experiments. However, since the ability to detect any running increaseswith the lever arm in comoving wavenumber, we conjecture that high redshift21 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 arecorrelated with the inflationary scale, and thus the amplitude of the CMBB mode.