CBR Anisotropy and the Running of the Scalar Spectral Index

Accurate ($\lesssim 1\mathrm{\%}$) predictions for the anisotropy of the Cosmic Background Radiation (CBR) are essential for using future high-resolution ($\lesssim 1^{\circ }$) CBR maps to test cosmological models. In many inflationary models the variation (``running’') of the spectral index of the spectrum of density perturbations is a significant effect and leads to changes of around 1% to 10% in the CBR power spectrum. We propose a general method for taking running into account which uses the derivative of the spectral index ($dn/d\ln k$)\mathrm{.}Conversely,high-resolutionCBRmapsmaybeabletodetermine$dn/d\ln k$, giving important information about the inflationary potential.