Constraints in cosmological parameter space from the Sunyaev-Zeldovich effect and thermal bremsstrahlung

We discuss how the space of possible cosmological parameters is constrained by the angular diameter distance function D_A(z) as measured using the SZ/X-ray method, which combines the Sunyaev-Zeldovich (SZ) effect and X-ray brightness data for clusters of galaxies. New X-ray satellites and ground-based interferometers dedicated to SZ observations should soon lead to D_A(z) measurements limited by systematic rather than random error. We analyze the systematic and random error budgets to make a realistic estimate of the accuracy achievable in the determination of (Ω _m, Ω_Λ, h), the density parameters of matter and cosmological constant, and the dimensionless Hubble constant, using D _A(z) derived from the SZ/X-ray method and the position of the first "Doppler" peak in the cosmic microwave background fluctuations. We briefly study the effect of systematic errors. We find that Ω _m, Ω_Λ, and w are affected, but h is not, by systematic errors that grow with redshift. With as few as 70 clusters, each providing a measurement of D_A(z) with a 7% random and 5% systematic error, Ω_m can be constrained to ±0.2, Ω _Λ to ±0.2, and h to ±0.11 (all at 3 σ). We also estimate constraints for the alternative three-parameter set (Ω_m, w, h), where w is the equation-of-state parameter. The measurement of D_A(z) provides constraints complementary to those from the number density of clusters in redshift space. A sample of 70 clusters (D_A measured with the same accuracy as before) combined with cluster evolution results (or a known matter density) can constrain w within ±0.45 (at 3 σ). Studies of X-ray and SZ properties of clusters of galaxies promise an independent and powerful test for cosmological parameters.