Impact of Point Source Clustering on Cosmological Parameters with CMB Anisotropies

The faint radio point sources that are unresolved in cosmic microwave background (CMB) anisotropy maps are likely to be a biased tracer of the large-scale structure dark matter distribution. While the shot-noise contribution to the angular power spectrum of unresolved radio point sources is included either when optimally constructing the CMB angular power spectrum, as with WMAP data, or when extracting cosmological parameters, we suggest that clustering part of the point source power spectrum should also be included. This is especially necessary at high frequencies above 150 GHz, where the clustering of far-IR sources is expected to dominate the shot-noise level of the angular power spectrum at tens of arcminute angular scales of both radio and sub-mm sources. We make an estimate of source clustering of unresolved radio sources in both WMAP and ACBAR, and marginalize over the amplitude of source clustering in each CMB data set when model fitting for cosmological parameters. For the combination of WMAP 5-year data and ACBAR, we find that the spectral index changes from the value of $0.963 \pm 0.014$ to $0.959 \pm 0.014$ (at 68% c.l.) when the clustering power spectrum of point sources is included in model fits. While we find that the differences are marginal with and without source clustering in current data, it may be necessary to account for source clustering with future datasets such as Planck, especially to properly model fit anisotropies at arcminute angular scales. If clustering is not accounted and point sources are modeled with a shot-noise only out to $l \sim 2000$, the spectral index will be biased by about 1.5$\sigma$.