Constraints on dark energy from the CSST galaxy clusters

We study the potential of the galaxy cluster sample expected from the China Space Station Telescope (CSST) survey to constrain dark energy properties. By modelling the distribution of observed cluster mass for a given true mass to be log-normal and adopting a selection threshold in the observed mass $M_{200m} \geq 0.836 \times 10^{14} h^{-1}M_{\odot}$, we find about $4.1 \times 10^{5}$ clusters in the redshift range $0 \leq z \leq 1.5$ can be detected by the CSST. We construct the Fisher matrix for the cluster number counts from CSST, and forecast constraints on dark energy parameters for models with constant ($w_0$CDM) and time dependent ($w_0w_a$CDM) equation of state. In the self-calibration scheme, the dark energy equation of state parameter $w_0$ of $w_0$CDM model can be constrained to $Δw_0 = 0.036$. If $w_a$ is added as a free parameter, we obtain $Δw_0 = 0.077$ and $Δw_a = 0.39$ for the $w_0w_a$CDM model, with a Figure of Merit for ($w_0,w_a$) to be 68.99. Should we had perfect knowledge of the observable-mass scaling relation (``known SR" scheme), we would obtain $Δw_0 = 0.012$ for $w_0$CDM model, $Δw_0 = 0.062$ and $Δw_a = 0.24$ for $w_0w_a$CDM model. The dark energy Figure of Merit of ($w_0,w_a$) increases to 343.25. By extending the maximum redshift of the clusters from $z_{max} \sim 1.5$ to $z_{max} \sim 2$, the dark energy Figure of Merit for ($w_0,w_a$) increases to 89.72 (self-calibration scheme) and 610.97 (``known SR" scheme), improved by a factor of $\sim 1.30$ and $\sim 1.78$, respectively. We find that the impact of clusters' redshift uncertainty on the dark energy constraints is negligible as long as the redshift error of clusters is smaller than 0.01, achievable by CSST. We also find that the bias in logarithm mass must be calibrated to be $0.30$ or better to avoid significant dark energy parameter bias.