On minimally parametric primordial power spectrum reconstruction and the evidence for ared tilt

Abstract

The latest cosmological data seem to indicate a significant deviation from scaleinvariance of the primordial power spectrum when parameterized either by apower law or by a spectral index with non-zero ‘running’. This deviation, byitself, serves as a powerful tool for discriminating among theories for the origin ofcosmological structures such as inflationary models. Here, we use a minimally parametricsmoothing spline technique to reconstruct the shape of the primordial power spectrum.This technique is well suited to searching for smooth features in the primordialpower spectrum such as deviations from scale invariance or a running spectralindex, although it would recover sharp features of high statistical significance.We use the WMAP three-year results in combination with data from a suiteof higher resolution cosmic microwave background experiments (including thelatest ACBAR 2008 release), as well as large-scale structure data from SDSS and2dFGRS. We employ cross-validation to assess, using the data themselves, theoptimal amount of smoothness in the primordial power spectrum consistent withthe data. This minimally parametric reconstruction supports the evidence fora power law primordial power spectrum with a red tilt, but not for deviationsfrom a power law power spectrum. Smooth variations in the primordial powerspectrum are not significantly degenerate with the other cosmological parameters.