The Sunyaev–Zel’dovich angular power spectrum as a probe of cosmological parameters

The angular power spectrum of the Sunyaev–Zel’dovich (SZ) effect is a powerful probe of cosmology. It is easier to detect than individual clusters in the field, is insensitive to observational selection effects and does not require a calibration between cluster mass and flux, reducing the systematic errors which dominate the cluster-counting constraints. It receives a dominant contribution from virialized cluster region between 20-40% of the virial radius and is thus relatively insensitive to the poorly known gas physics in the cluster center, such as cooling or (pre)heating. In this paper we derive a refined analytic prediction for the SZ angular power spectrum using the universal gasdensity and temperature profile and the dark-matter halo mass function. The predicted power spectrum has no free parameters and fits all of the published hydrodynamic simulation results to better than a factor of two for l < 10000. We find that the angular power spectrum Cl scales as Cl ∝ σ 7 8(Ωbh) 2 and is almost independent of all of the other cosmological parameters. This differs from the local cluster abundance studies, which give a relation between σ8 and Ωm. We also compute the covariance matrix of Cl using the halo model and find a good agreement relative to the simulations. We argue that the best constraint from the SZ power spectrum comes from l ∼ 3000, where the sampling variance is sufficiently small and the spectrum is dominated by massive clusters above 10 h M⊙ for which cooling, heating and details of star formation are not very important. We estimate how well we can determine σ8(Ωbh) 2/7 with sampling-variance-limited observations and find that for a several-square-degree survey with arcminute resolution one should be able to determine σ8 to within a few percent, with the remaining uncertainty dominated by theoretical modelling. If the recent excess of the CMB power on small scales reported by the CBI experiment is due to the SZ effect, then we find σ8(Ωbh/0.035) 0.3 = 1.05 ± 0.15 at 95% confidence level (statistical) and with a residual 10% systematic (theoretical) uncertainty.