Detailed analyses of the WMAP data indicate possible oscillatory features in the primordial curvature perturbation, which moreover appears to be suppressed beyond the present Hubble radius. Such deviations from the usual inflationary expectation of an approximately Harrison-Zeldovich spectrum are expected in the supergravity-based “multiple inflation” model wherein phase transitions during inflation induce sudden changes in the mass of the inflaton, thus interrupting its slow roll. In a previous paper we calculated the resulting curvature perturbation and showed how the oscillations arise. Here we perform a Markov chain Monte Carlo fitting exercise using the 3-year WMAP data to determine how the fitted cosmological parameters vary when such a primordial spectrum is used as an input, rather than the usually assumed power-law spectrum. The concordance $\Lambda \mathrm{CDM}$ model is still a good fit when there is just a step in the spectrum. However, if there is a bump in the spectrum (due e.g. to two phase transitions in rapid succession), the precision cosmic microwave background data can be well fitted by a flat Einstein-de Sitter cosmology without dark energy. This however requires the Hubble constant to be $h\simeq 0.44$ which is lower than the locally measured value. To fit the Sloane Digital Sky Survey data on the power spectrum of galaxy clustering requires a $\sim 10\%$ component of hot dark matter, as would naturally be provided by 3 species of neutrinos of mass $\sim 0.5\mathrm{eV}$. This $\mathrm{\text{cold}}+\mathrm{\text{hot dark matter}}$ model cannot however fit the position of the baryon acoustic peak in the luminous red galaxies redshift two-point correlation function. It may be possible to overcome these difficulties in an inhomogeneous Lemaître-Tolman-Bondi cosmological model with a local void, which can potentially also account for the SN Ia Hubble diagram without invoking cosmic acceleration.

• Received 26 June 2007

DOI:https://doi.org/10.1103/PhysRevD.76.123504