Bumpy power spectra and ΔT/T

With the recent publication of the measurements of the radiation angular power spectrum from the BOOMERanG-98 Antarctic flight, it has become apparent that the currently favoured spatially flat cold dark matter model (matter density parameter Ω_m = 0.3, flatness being restored by a cosmological constant Ω_Λ = 0.7, Hubble parameter h = 0.65, baryon density parameter Ω_bh² = 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 k_b and characterized by a Gaussian in log k of standard deviation σ_b and amplitude A_b, which is superimposed on to a scale-invariant power spectrum. We generate a range of theoretical models that include a bump at scales consistent with cosmic microwave background (CMB) and large-scale structure observations, and perform a simple _X² test to compare our models with the COBE Differential Microwave Radiometer (DMR) data and the recently published BOOMERanG-98 and MAXIMA-1 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 cut-off on the high ℓ side of the first acoustic peak. Current galaxy redshift survey data suggest that excess power is required at a scale around 100 Mpc, corresponding to k_b ∼ 0.05 h Mpc^-1. For the concordance model, use of a bump-like feature to account for this excess is not consistent with the constraints imposed by recent CMB data. We note that models with an appropriately chosen break in the power spectrum provide an alternative model that can give distortions similar to those reported in the automated plate measurement (APM) survey as well as consistency with the CMB data. We prefer, however, to discount the APM data in favour of the less biased decorrelated linear power spectrum recently constructed from the Point Source Catalogue Redshift (PSCz) redshift survey. We show that the concordance cosmology can be resurrected using our phenomenological approach and that our best-fitting model is in agreement with the PSCz observations.