Constraints on Dark Energy from Galaxy Cluster Gas Mass Fraction versus Redshift data

We use the Allen et al. (2008) galaxy cluster gas mass fraction versus redshift data to constrain parameters of three different dark energy models: a cosmological constant dominated one ($\Lambda$CDM); the XCDM parameterization of dark energy; and a slowly-rolling scalar field model with inverse-power-law potential energy density. (Instead of using the Monte Carlo Markov Chain method, when integrating over nuisance parameters we use an alternative method of introducing an auxiliary random variable.) The resulting constraints are consistent with, and typically more constraining than, those derived from other cosmological data. A time-independent cosmological constant is a good fit to the galaxy cluster data, but slowly evolving dark energy cannot yet be ruled out.