  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 ~ 3e-4 /Mpc 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 <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 ~< 0.15, with a hint of a decrease in power
on the largest scales.
