CBR Anisotropy and the Running of the Scalar Spectral Index

TL;DR

A general method for taking running into account which uses the derivative of the spectral index (dn/dlnk) is proposed, which suggests that high-resolution CBR maps may be able to determine dn/ dlnk, giving important information about the inflationary potential.

Abstract

Accurate ($\lesssim 1\% $) predictions for the anisotropy of the Cosmic Background Radiation (CBR) are essential for using future high-resolution ($\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$). Conversely, high-resolution CBR maps may be able to determine $dn/d\ln k$, giving important information about the inflationary potential.

Figures (1)

• Figure 1: Predicted angular power spectra for $b=6$ chaotic inflation with (solid) and without (broken) the running of the scalar spectral index ($n=0.92$, $h=0.7$, $\Omega_B = 0.025$, and $dn/d\ln k = -0.002$).