Observational constraints on the spectral index of the cosmological curvature perturbation

We evaluate the observational constraints on the spectral index n, in the context of the $\Lambda \mathrm{CDM}$ hypothesis which represents the simplest viable cosmology. We first take n to be practically scale independent. Ignoring reionization, we find at a nominal $2-\sigma$ level $n\simeq 1.0\pm \mathrm{0.1.}$ If we make the more realistic assumption that reionization occurs when a fraction $f\sim {10}^{-5}$ to $1$ of the matter has collapsed, the $2-\sigma$ lower bound is unchanged while the $1-\sigma$ bound rises slightly. These constraints are compared with the prediction of various inflation models. Then we investigate the two-parameter scale-dependent spectral index, predicted by running-mass inflation models, and find that present data allow significant scale dependence of n, which occurs in a physically reasonable regime of parameter space.