Bumpy Power Spectra and ∆T/T

With the recent publication of the measurements of the radiation angular power spectrum from the BOOMERanG Antarctic flight (de Bernardis et al. 2000), it has become apparent that the currently favoured spatially–flat cold dark matter model (matter density parameter Ωm = 0.3, flatness being restored by a cosmological constant ΩΛ = 0.7, Hubble parameter h = 0.65, baryon density parameter Ωbh 2 = 0.02) no longer provides a good fit to the data. We describe a phenomenological approach to resurrecting this paradigm. We consider a primordial power spectrum which incorporates a bump, arbitrarily placed at kb, and characterized by a Gaussian in log k of standard deviation σb and amplitude Ab, that is superimposed onto a scale–invariant power spectrum. We generate a range of theoretical models that include a bump at scales consistent with cosmic microwave background and large–scale structure observations, and perform a simple χ test to compare our models with the COBE DMR data and the recently published BOOMERanG and MAXIMA data. Unlike models that include a high baryon content, our models predict a low third acoustic peak. We find that low l observations (20 < l < 200) are a critical discriminant of the bumps because the transfer function has a sharp cutoff on the high l side of the first acoustic peak. Current galaxy redshift survey data suggests that excess power is required at a scale around 100 Mpc, corresponding to kb ∼ 0.05 h Mpc . For the concordance model, use of a bump–like feature to account for this excess is not consistent with the constraints made from recent CMB data. We note that models with an appropriately chosen break in the power spectrum provide an alternative toy model that can give distortions similar to those reported in the APM survey as well as consistency with the CMB data (Atrio-Barandela 2000; Sarkar 2000). We prefer however to discount the APM data in favour of the less biased decorrelated linear power spectrum recently constructed from the PSCz redshift survey (Hamilton & Tegmark 2000). We show that the concordance cosmology can be resurrected using our phenomenological approach and our best-fitting model is in agreement with the PSCz observations.