  We present a Bayesian analysis of large-scale structure and cosmic microwave
background data to constrain the form of the primordial power spectrum. We have
extended the usual presumption of a scale invariant spectrum to include: (i) a
running spectral index; (ii) a broken spectrum arising perhaps from an
interruption of the potential driving inflation; (iii) a large scale cutoff in
power as the first year WMAP results appear to indicate; (iv) a reconstruction
of the spectrum in eight bins in wavenumber; and (v) a spectrum resulting from
a cosmological model proposed by Lasenby & Doran, which naturally exhibits an
exponential drop in power on very large scales. The result of our complete
Bayesian analysis includes not only the posterior probability distribution from
which parameter estimates are inferred but also the Bayesian evidence. This
evidence value is greater for a model with fewer parameters unless a more
complicated model provides a significantly better fit to the data, thus
allowing a powerful method of model selection. We find that those models
exhibiting any form of cutoff in power on large scales consistently produce
higher evidences than either the Harrison-Zel'dovich or single spectral index
spectra. In particular, within the best-fit concordance cosmology, we find the
Lasenby & Doran spectrum to show significantly larger evidence as compared to
the other models.
