Reconstructing the primordial power spectrum

We reconstruct the shape of the primordial power spectrum from the latest cosmic microwave background data, including the new results from the Wilkinson Microwave Anisotropy Probe, and large scale structure data from the two degree field galaxy redshift survey. We have tested three parameterizations taking into account the uncertainties in four cosmological parameters and find consistent results from each. First we parameterize the initial spectrum by a tilt and a running spectral index, finding results in agreement with the WMAP team (marginal 1. 3 sigma evidence for a running spectral index). Secondly we use a model independent parameterization, with 16 bands in wavenumber, and find no obvious sign of deviation from scale invariance. Furthermore the values of the other cosmological parameters defining the model remain relatively well constrained despite the freedom in the shape of the initial power spectrum. Finally we investigate a model, motivated by double inflation, in which the power spectrum has a break between two characteristic wavenumbers. We find that if a break is required to be in the range 0. 01 < k / Mpc^-1 < 0. 1 then the ratio of amplitudes across the break is constrained to be 1. 21 +/- 0. 12. These results provide powerful new evidence that the primordial power spectrum is featureless and close to scale invariant over the wavenumber range 0. 005 ~< k /Mpc^-1 ~< 0. 15.