COSMOLOGICAL PARAMETER-ESTIMATION AND THE SPECTRAL INDEX FROM INFLATION

Accurate estimation of cosmological parameters from microwave backgrou nd anisotropies requires high-accuracy understanding of the cosmologic al model. Normally, a power-law spectrum of density perturbations is a ssumed, in which case the spectral index n can be measured to around /-0.004 using microwave anisotropy satellites such as MAP and Planck. However, inflationary models generically predict that the spectral ind ex n of the density perturbation spectrum will be scale-dependent. We carry out a detailed investigation of the measurability of this scale dependence by Planck, including the influence of polarization on the p arameter estimation. We also estimate the increase in the uncertainty in all other parameters if the scale dependence has to be included. Th is increase applies even if the scale dependence is too small to be me asured, unless it is assumed absent. We study the implications for inf lation models, beginning with a brief examination of the generic slow- roll inflation situation, and then move to a detailed examination of a recently devised hybrid inflation model for which the scale dependenc e of n may be observable.