WMAP 3-yr primordial power spectrum

We constrain the form of the primordial power spectrum using Wilkinson Microwave Anisotropy Probe (WMAP) 3-yr cosmic microwave background (CMB) data (plus other high resolution CMB experiments) in addition to complementary large-scale structure (LSS) data: 2dF, Sloan Digital Sky Survey (SDSS), Ly alpha forest and luminous red galaxy (LRG) data from the SDSS catalogue. We extend the work of the WMAP team to that of a fully Bayesian approach whereby we compute the comparative Bayesian evidence in addition to parameter estimates for a collection of seven models: (i) a scale-invariant Harrison -Zel'dovich (HZ) spectrum; (ii) a power law; (iii) a running spectral index; (iv) a broken spectrum; (v) a power law with an abrupt cut-off on large scales; (vi) a reconstruction of the spectrum in eight bins in wavenumber and (vii) a spectrum resulting from a cosmological model proposed by Lasenby & Doran (LD). Using a basic data set of WMAP3 + other CMB + 2dF + SDSS, our analysis confirms that a scale-invariant spectrum is disfavoured by between 0.7 and 1.7 units of log evidence (depending on priors chosen) when compared with a power-law tilt. Moreover, a running spectrum is now significantly preferred, but only when using the most constraining set of priors. The addition of both Ly alpha and LRG data independently suggests much lower values of the running index than with basic data set alone, and interestingly the inclusion of Ly alpha significantly disfavours a running parametrization by more than a unit in log evidence. Overall, the highest evidences, over all data sets, were obtained with a power-law spectrum containing a cut-off with a significant log evidence difference of roughly 2 units. The natural tilt and exponential cut-off present in the LD spectrum is found to be favoured decisively by a log evidence difference of over 5 units, but only for a limited study within the best-fitting concordance cosmology.