Abstract
The first-year WMAP measurement of the cosmic microwave background (CMB) temperature anisotropy is intriguingly consistent with a larger running of the inflationary scalar spectral index than would be expected for single-field inflation. We revisit the issue of a large running spectral index, first by re-examining the evidence from the data, and then by reconstructing the inflationary potential, using an improved method based upon the Hamilton–Jacobi formulation. We note that a spectrum which runs only over 1.5 decades of k space provides as good a fit to the CMB data as one which runs at all k, that significant evidence for running comes from multipoles l near 40, and that large running gives a better fit than a flat spectrum primarily if the tensor-to-scalar ratio r is large, r∼0.5, and the field values are at the Planck scale. This allows one to break the large degeneracy of potentials which would be consistent with the scalar power alone. Large running, should it be confirmed, is thus linked to a high scale of inflation and the possibility of seeing effects of tensor modes in the CMB and Planck-scale physics. Nevertheless, we show that the reconstructed inflaton potential is well described by a renormalizable potential whose quantum corrections are under control despite the large field values.