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 two degree field galaxy redshift survey ( 2dFGRS ) .
We tested four parameterizations taking into account the uncertainties in four cosmological parameters .
First we parameterize 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 ( \ell = 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 k _ { c } \sim 3 \times 10 ^ { -4 } { Mpc } ^ { -1 } although k _ { c } = 0 ( no cut ) is not ruled out .
Thirdly we use a model independent parameterization , 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 \pm 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 \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } k / { Mpc ^ { -1 } } \lower 2.1 % 5 pt \hbox { $ \buildrel < \over { \sim } $ } 0.15 , with a hint of a decrease in power on the largest scales .