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 ΛCDM hypothesis which represents the simplest viable cosmology. We first take n to be practically scale independent. Ignoring reionization, we find at a nominal 2-σ level n≃1.0±0.1. If we make the more realistic assumption that reionization occurs when a fraction f∼10^-5 to 1 of the matter has collapsed, the 2-σ lower bound is unchanged while the 1-σ 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.