  We constrain the form of the primordial power spectrum using Wilkinson
Microwave Anisotropy Probe (WMAP) 3-year cosmic microwave background (CMB) data
(+ other high resolution CMB experiments) in addition to complementary
large-scale structure (LSS) data: 2dF, SDSS, Ly-alpha forest and luminous red
galaxy (LRG) data from the SDSS catalogue. We compute the comparative Bayesian
evidence in addition to parameter estimates for a collection of seven models:
(i) a scale invariant Harrison-Zel'dovich (H-Z) spectrum; (ii) a power-law;
(iii) a running spectral index; (iv) a broken spectrum; (v) a power-law with an
abrupt cutoff 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 (L-D). Using a basic dataset 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 Ly-alpha and LRG data independently both suggest much
lower values of the running index than with basic dataset alone and
interestingly the inclusion of Ly-alpha significantly disfavours a running
parameterisation by more than a unit in log evidence. Overall the highest
evidences, over all datasets, were obtained with a power law spectrum
containing a cutoff with a significant log evidence difference of roughly 2
units. The natural tilt and exponential cutoff present in the L-D 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-fit concordance cosmology.
