Running of the scalar spectral index from inflationary models

Abstract

The scalar spectral index n is an important parameter describing the nature of primordial density perturbations. Recent data, including those from the Wilkinson Microwave Anisotropy Probe satellite, show some evidence that the index runs (changes as a function of the scale k at which it is measured) from $ng1$ (blue) on long scales to $nl1$ (red) on short scales. We investigate the extent to which inflationary models can accommodate such significant running of n. We present several methods for constructing large classes of potentials which yield a running spectral index. We show that within the slow-roll approximation, the fact that $n\ensuremath{-}1$ changes sign from blue to red forces the slope of the potential to reach a minimum at a similar field location. We also briefly survey the running of the index in a wider class of inflationary models, including a subset of those with nonminimal kinetic terms.