Are clusters standard candles? Galaxy cluster scaling relations with the Sunyaev-Zeldovich effect

An extensive sample of galaxy clusters will be available in the coming years, detected through their Sunyaev-Zeldovich effect (SZE). We use a semianalytic model to study the scientific yield of combining SZE data with X-ray and optical follow-up observations. If clusters at a given redshift z(0) can be identified with virialized, spherical halos, they populate a well-defined "fundamental plane" (FP) in the parameter space of the three observables virial temperature (T), total Sunyaev-Zeldovich flux decrement (DeltaS(nu)), and angular size (theta). The location and orientation of the FP, as well as its redshift evolution, are sensitive to both the internal evolution of clusters and to the underlying cosmological parameters. We show that if clusters are not standard candles (e.g., because of feedback or energy injection), then this can be inferred from the FP. Likewise, we study the dependence of the FP on the cosmological parameters h, sigma(8), and Omega(0), and quantify future constraints on these parameters. We also show that in the absence of any nongravitational effects, the scatter in the (DeltaS(nu); T)-plane is significantly smaller than in either the (theta,T) or the (theta, DeltaS(nu)) planes. As a result, the DeltaS(nu)-T relation can be an exceptionally sensitive probe of both cluster physics and cosmological parameters. A comparison of the amount of scatter in these three scaling relations will test the origin (cosmological vs. stochastic) of the scatter.