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Detailed analyses of the WMAP data indicate possible oscillatory features inthe primordial curvature perturbation, which moreover appears to be suppressedbeyond the present Hubble radius. Such deviations from the usual inflationaryexpectation of an approximately Harrison-Zeldovich spectrum are expected in thesupergravity-based 'multiple inflation' model wherein phase transitions duringinflation induce sudden changes in the mass of the inflaton, thus interruptingits slow-roll. In a previous paper we calculated the resulting curvatureperturbation and showed how the oscillations arise. Here we perform a MarkovChain Monte Carlo fitting exercise using the 3-year WMAP data to determine howthe fitted cosmological parameters vary when such a primordial spectrum is usedas an input, rather than the usually assumed power-law spectrum. The'concordance' LCDM model is still a good fit when there is just a 'step' in thespectrum. However if there is a 'bump' in the spectrum (due e.g. to two phasetransitions in rapid succession), the precision CMB data can be well-fitted bya flat Einstein-de Sitter cosmology without dark energy. This however requiresthe Hubble constant to be h ~ 0.44 which is lower than the locally measuredvalue. To fit the SDSS data on the power spectrum of galaxy clustering requiresa ~10% component of hot dark matter, as would naturally be provided by 3species of neutrinos of mass ~0.5 eV. This CHDM model cannot however fit theposition of the baryon acoustic peak in the LRG redshift two-point correlationfunction. It may be possible to overcome these difficulties in an inhomogeneousLemaitre-Tolman-Bondi cosmological model with a local void, which canpotentially also account for the SN Ia Hubble diagram without invoking cosmicacceleration.

Multiple inflation and the WMAP 'glitches' II. Data analysis and cosmological parameter extraction