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 (WMAP), and large-scale structure data from the 2 Degree Field Galaxy Redshift Survey (2dFGRS). We tested four parametrizations, taking into account the uncertainties in four cosmological parameters. First we parametrize the initial spectrum by a tilt and a running spectral index, finding marginal evidence for a running spectral index only if the first three WMAP multipoles (l = 2, 3, 4) are included in the analysis. Secondly, to investigate further the low CMB large-scale power, we modify the conventional power-law spectrum by introducing a scale above which there is no power. We find a preferred position of the cut at kc ∼ 3 × 10 -4 Mpc-1, although kc = 0 (no cut) is not ruled out. Thirdly, we use a model independent parametrization, with 16 bands in wavenumber, and find no obvious sign of deviation from a power-law spectrum on the scales investigated. 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 1.23 ± 0.14. Our results are consistent with a power-law spectrum that is featureless and close to scale invariant over the wavenumber range 0.005 ≲ k/Mpc-1 ≲ 0.15, with a hint of a decrease in power on the largest scales.