Constraining nonstandard recombination: A worked example

We fit the BOOMERANG, MAXIMA and COBE-DMR measurements of the cosmic microwave background anisotropy in spatially flat cosmological models where departures from standard recombination of the primeval plasma are parametrized through a change in the fine structure constant $\alpha$ compared to its present value. In addition to $\alpha$ we vary the baryon and dark matter densities, the spectral index of scalar fluctuations, and the Hubble constant. Within the class of models considered, the lack of a prominent second acoustic peak in the measured spectrum can be accommodated either by a relatively large baryon density, by a tilt towards the red in the spectrum of density fluctuations, or by a delay in the time at which neutral hydrogen formed. The ratio between the second and first peak decreases by around 25% either if the baryon density ${\Omega }_b{h}^2$ is increased or the spectral index n decreased by a comparable amount, or if neutral hydrogen formed at a redshift $z_{*}$ about 15% smaller than its standard value. We find that the present data are best fitted by a delay in recombination, with a lower baryon density than the best fit if recombination is standard. Our best fit model has $z_{*}=900,\hspace{0.5em}{\Omega }_b{h}^2=0.024,\hspace{0.5em}{\Omega }_m{h}^2=0.14,\hspace{0.5em}{H}_0=49\mathrm{}$ and $n=\mathrm{1.02.}\mathrm{}$ Compatible with present data at 95% confidence level $780<\mathrm{}{z}_{*}<1150,\hspace{0.5em}0.018<\mathrm{}{\Omega }_b{h}^2<0.036,\hspace{0.5em}0.07<\mathrm{}{\Omega }_m{h}^2<0.3\mathrm{}$ and $0.9<n<\mathrm{}\mathrm{1.2.}\mathrm{}$