Observational constraints on the spectral index of the cosmological curvature perturbation

We have evaluated the observational constraints on the spectral index $n$, in the context of the $\Lambda$CDM model which is the simplest viable choice. If $n$ is practically scale-independent, as predicted by most models of inflation, present data require $n\simeq 1.0 \pm 0.1$ at something like the 2-$\sigma$ level. We also exhibit the much tighter constraint, obtained if one fixes the epoch of reionization, and the height of the first acoustic peak in the cmb anisotropy. The former has a preferred range 20 to 30, while the latter may soon be accurately known. We have also investigated the two-parameter scale-dependent spectral index, predicted by running-mass inflation models. Present data allow significant variation of of $n$ in this case, which occurs in a physically reasonable regime of parameter space.