Model-Independent Reconstruction of the Primordial Power Spectrum from WMAP Data

Reconstructing the shape of the primordial power spectrum in a model independent way from cosmological data is a useful consistency check on what is usually assumed regarding early universe physics. It is also our primary window to unknown physics during the inflationary era. Using a power-law form for the primordial power spectrum $P_{in}(k)$ and constraining the scalar spectral index and its running, \cite{Peiris03} found that the first year WMAP data seem to indicate a preferred scale in $P_{in}(k)$. We use two complementary methods: the wavelet band powers method of \cite{pia1}, and the top-hat binning method of \cite{Wang99} to reconstruct $P_{in}(k)$ as a free function from CMB data alone (WMAP, CBI, and ACBAR), or from CMB data together with large scale structure data (2dFGRS and PCSZ). The shape of the reconstructed $P_{in}(k)$ is consistent with scale-invariance, although it allows some indication of a preferred scale at $k \sim 0.01$Mpc$^{-1}$. While consistent with the possible evidence for a running of the scalar spectral index found by the WMAP team, our results highlight the need of more stringent and independent constraints on cosmological parameters (the Hubble constant in particular) in order to more definitively constrain deviations of $P_{in}(k)$ from scale-invariance without making assumptions about the inflationary model.