  The first year WMAP measurement of the 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 reexamining 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.
