CBR anisotropy and the running of the scalar spectral index

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Abstract
Accurate (≲1%) predictions for the anisotropy of the cosmic background radiation (CBR) are essential for using future high-resolution (≲1°) 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 1–10 % in the CBR power spectrum. We propose a general method for taking running into account which uses the derivative of the spectral index (dn/dlnk). Conversely, high-resolution CBR maps may be able to determine dn/dlnk, giving important information about the inflationary potential.