• galaxies: clusters: general;
  • galaxies: haloes;
  • cosmic microwave background;
  • cosmological parameters;
  • cosmology: theory;
  • dark matter


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 that dominate the cluster-counting constraints. It receives a dominant contribution from virialized cluster region between 20 and 40 per cent of the virial radius and is thus relatively insensitive to the poorly known gas physics in the cluster centre, such as cooling or (pre)heating. In this paper we derive a refined analytic prediction for the SZ angular power spectrum using the universal gas density 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 2 for 2000 < l < 10 000. We find that the angular power spectrum Cl scales as Cl∝σ78bh)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 1014h−1 M for which cooling, heating and details of star formation are not very important. We estimate how well we can determine σ8bh)2/7 with sampling-variance-limited observations and find that for a several-square-degree survey with arcmin resolution one should be able to determine σ8 to within a few per cent, with the remaining uncertainty dominated by theoretical modelling. If the recent excess of the cosmic microwave background power on small scales reported by Cosmic Background Imager (CBI) and Berkeley Illinois Maryland Association (BIMA) experiments is due to the SZ effect, then we find σ8bh/0.035)0.29= 1.04 ± 0.12 at 95 per cent confidence level (statistical) and with a residual 10 per cent systematic (theoretical) uncertainty.