Primordial power spectrum from WMAP

The observed angular power spectrum of the cosmic microwave background temperature anisotropy, $C_l,$ is a convolution of a cosmological radiative transport kernel with an assumed primordial power spectrum of inhomogeneities. Exquisite measurements of $C_l$ over a wide range of multipoles from the Wilkinson Microwave Anisotropy Probe (WMAP) has opened up the possibility to deconvolve the primordial power spectrum for a given set of cosmological parameters (base model). We implement an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from WMAP assuming the concordance cosmological model. The most prominent feature of the recovered $P\left(k\right)\mathrm{}$ is a sharp, infrared cutoff on the horizon scale. The resultant $C_l$ spectrum using the recovered spectrum has a likelihood far better than a scale invariant, or, “best fit” scale free spectra $(\Delta \ln \mathcal{L}\approx 25$ with respect to Harrison Zeldovich, and, $\Delta \ln \mathcal{L}\approx 11$ with respect to power law with $n_s=0.95).\mathrm{}$ The recovered $P\left(k\right)\mathrm{}$ has a localized excess just above the cutoff which leads to great improvement of likelihood over the simple monotonic forms of model infrared cutoff spectra considered in the post WMAP literature. The recovered $P\left(k\right),$ in particular, the form of infrared cutoff is robust to small changes in the cosmological parameters. We show that remarkably similar form of infrared cutoff is known to arise in very reasonable extensions and refinements of the predictions from simple inflationary scenarios. Our method can be extended to other cosmological observations such as the measured matter power spectrum and, in particular, the much awaited polarization spectrum from WMAP.