Global fits for the spectral index of the cosmological curvature perturbation

Abstract

Best-fit values of the spectral index of the curvature perturbation are presented, assuming the $Λ$CDM cosmology. Apart from the spectral index, the parameters are the Hubble parameter, the total matter density and the baryon density. The data points are intended to represent all measurements which are likely to significantly affect the result. The cosmic microwave anisotropy is represented by the COBE normalization, and heights of the first and second peaks given by the latest Boomerang and Maxima data. The slope of the galaxy correlation function and the matter density contrast on the $8h^{-1}\Mpc$ scale are each represented by a data point, as are the expected values of the Hubble parameter and matter density. The `low-deuterium' nucleosynthesis value of the baryon density provides a final data point, the fit giving a value about one standard deviation higher. The reionization epoch is calculated from the model by assuming that it corresponds to the collapse of a fraction $f\gsim 10^{-4}$ of matter. We consider the case of a scale-independent spectral index, and also the scale-dependent spectral index predicted by running mass models of inflation. In the former case, the result is compared with the prediction of models of inflation based on effective field theory, in which the field value is small on the Planck scale. Detailed comparison is made with other fits, and other approaches to the comparison with theory.