Accurate estimation of cosmological parameters from microwave background
anisotropies requires high-accuracy understanding of the cosmological model.
Normally, a power-law spectrum of density perturbations is assumed, 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 index 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 parameter estimation. We also
estimate the increase in the uncertainty in all other parameters if the scale
dependence has to be included. This increase applies even if the scale
dependence is too small to be measured unless it is assumed absent, but is
shown to be a small effect. We study the implications for inflation 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 dependence of n may be observable.Comment: 6 pages LaTeX file with one figure incorporated (uses mn.sty and
epsf). Important modifications to result