Running of the scalar spectral index from inflationary models

The scalar spectral index n is an important parameter describing the natureof primordial density perturbations. Recent data, including that from the WMAPsatellite, shows some evidence that the index runs (changes as a function ofthe scale k at which it is measured) from n>1 (blue) on long scales to n<1(red) on short scales. We investigate the extent to which inflationary modelscan accomodate such significant running of n. We present several methods forconstructing large classes of potentials which yield a running spectral index.We show that within the slow-roll approximation, the fact that n-1 changes signfrom blue to red forces the slope of the potential to reach a minimum at asimilar field location. We also briefly survey the running of the index in awider class of inflationary models, including a subset of those withnon-minimial kinetic terms.Comment: 39 pages, 4 figures, references adde