Forecasting Constraint on Primordial Black Hole Properties with the CSST $3\times2$pt Analysis

This study forecasts the constraints on the properties of primordial black holes (PBHs) as a cold dark matter component using the galaxy clustering, weak lensing, and galaxy-galaxy lensing (i.e. $3\times2$pt) measurements from the upcoming Chinese Space Station Survey Telescope (CSST) photometric survey. Since PBHs formed via gravitational collapse in the early Universe, they can additionally affect the formation and evolution of the cosmic large-scale structure (LSS) through ``Poisson" effect. We compute the angular power spectra for PBH-$\Lambda$CDM cosmology, and generate mock data based on the CSST instrumental and survey design. The Markov Chain Monte Carlo (MCMC) method is employed to constrain the free parameters, such as the product of the PBH fraction and mass $f_{\rm PBH}m_{\rm PBH}$ and other cosmological parameters. The systematic parameters are also included in the fitting process, such as the parameters of the baryonic effect, intrinsic alignment, galaxy bias, photometric redshift (photo-$z$) calibration, shear calibration, and noise terms. We find that the CSST 3$\times$2pt analysis can achieve tight constraints on $f_{\rm PBH}m_{\rm PBH}$, with 68% and 95% confidence levels (CLs) reaching $<10^{3.9} M_{\odot}$ and $<10^{4.7} M_{\odot}$, respectively. Additionally, the cosmological parameters, e.g. $\Omega_m$, $\sigma_8$ and $w$, can be constrained with the precisions of 3.3%, 1.7%, 13%, respectively. This indicates that the CSST 3$\times$2pt analysis is a powerful tool to advance the PBH dark matter studies in the near future.