Inflationary potential reconstruction for a Wilkinson Microwave Anisotropy Probe runningpower spectrum

Abstract

The first-year WMAP measurement of the cosmic microwave background (CMB) temperatureanisotropy is intriguingly consistent with a larger running of the inflationary scalar spectralindex than would be expected for single-field inflation. We revisit the issue of a largerunning spectral index, first by re-examining the evidence from the data, and then byreconstructing the inflationary potential, using an improved method based upon theHamilton–Jacobi formulation. We note that a spectrum which runs only over 1.5 decades ofk space provides as good a fit to the CMB data as one which runs at allk, that significant evidence for running comes from multipolesl near40, and that large running gives a better fit than a flat spectrum primarily if the tensor-to-scalar ratior islarge, r∼0.5, and the field values are at the Planck scale. This allows one to break the large degeneracyof potentials which would be consistent with the scalar power alone. Large running, shouldit be confirmed, is thus linked to a high scale of inflation and the possibility of seeing effectsof tensor modes in the CMB and Planck-scale physics. Nevertheless, we showthat the reconstructed inflaton potential is well described by a renormalizablepotential whose quantum corrections are under control despite the large field values.