Testing cosmic acceleration for $w(z)$ parameterizations using $f_{gas}$ measurements in galaxy clusters

In this paper we study the cosmic acceleration for five dynamical dark energy models whose equation of state varies with redshift. The cosmological parameters of these models are constrained by performing a MCMC analysis using mainly gas mass fraction, $f_{gas}$, measurements in two samples of galaxy clusters: one reported by Allen et al. (2004), which consists of $42$ points spanning the redshift range $0.05<z<1.1$, and the other by Hasselfield et al. (2013) from the Atacama Cosmology Telescope survey, which consists of $91$ data points in the redshift range $0.118 < \mathrm{z} < 1.36$. In addition, we perform a joint analysis with the measurements of the Hubble parameter $H(z)$, baryon acoustic oscillations and the cosmic microwave background radiation from WMAP and Planck measurements to estimate the equation of state parameters. We obtained that both $f_{gas}$ samples provide consistent constraints on the cosmological parameters. We found that the $f_{gas}$ data is consistent at the $2\sigma$ confidence level with a cosmic slowing down of the acceleration at late times for most of the parameterizations. The constraints of the joint analysis using WMAP and Planck measurements show that this trend disappears. We have confirmed that the $f_{gas}$ probe provides competitive constraints on the dark energy parameters when a $w(z)$ is assumed.