On the better constraints from the South Pole Telescope Sunyaev-Zel'dovich galaxy clusters survey: a FoM evaluation for the equation of state of Dark Energy

In a recent article by Benson et al., 2011, the authors show the latest measurements from the South Pole Telescope (SPT) Sunyaev Zel'dovich (SZ) cluster survey to better constrain some cosmological parameters. In particular, the authors found that adding the SPT cluster data significantly improves the constraints on equation of state of dark energy, w, beyond those found when using measurements of the CMB, supernovae, BAO and the Hubble constant. The main aim of the present research note is to give a further quantitative estimation of the above better constraints, through the computation of the Figure of Merit (FoM) applied to \Omega_m and w plots for the 68% and 95% confidence regions. This allows a better evaluation and a better comparison of the continuous improvements on the cosmological constraints, obtained using new different cosmological probes and different surveys.