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

TL;DR

This work addresses whether primordial black holes (PBHs) can constitute cold dark matter by leveraging CSST 3x2pt measurements of galaxy clustering, weak lensing, and galaxy-galaxy lensing. It builds a PBH-LCDM framework incorporating PBH isocurvature perturbations into the total matter power spectrum and generates CSST-like mock angular power spectra, fitting them with MCMC while marginalizing over key systematics. The analysis forecasts that CSST 3x2pt can bound the PBH mass–fraction product to log10(f_PBH m_PBH / M_sun + 1) < 3.9 (68%) and < 4.7 (95%), with Omega_m, sigma_8, and w constrained at ~3.3%, 1.7%, and 13% respectively; the constraint is primarily driven by the small-scale shear signal. Overall, CSST 3x2pt offers strong potential to probe massive PBHs and to tighten large-scale structure constraints in the near future.

Abstract

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 the ``Poisson" effect. We compute the angular power spectra for PBH-$Λ$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. $Ω_m$, $σ_8$ 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.

Figures (10)

• Figure 1: The total PBH-$\Lambda$CDM power spectra (solid curves) and PBH isocurvature power spectra (dotted lines) in the PBH-$\Lambda$CDM model at $z = 0$ with $f_{\rm PBH} = 1$ for the three PBH masses, i.e. $m_{\rm PBH}=10^4$ (green), $10^5$ (blue), and $10^6M_{\odot}$ (red). The ratio of the PBH-$\Lambda$CDM and $\Lambda$CDM matter power spectrum for each $m_{\rm PBH}$ is also shown in the lower panel.
• Figure 2: The adopted galaxy redshift distributions in the CSST photometric survey. The black dotted curve shows the normalized total galaxy redshift distribution $n_{\rm g}(z)$, and the blue, orange, green, and red curves denote the galaxy redshift distribution in the four tomographic bins.
• Figure 3: The theoretical curves and mock data of the galaxy angular power spectra in different tomographic bins for the CSST 3$\times$2pt analysis. The blue solid curves represent the fiducial theoretical predictions. The red data points show the mock data used, while the gray data points indicate the excluded data with the signal-to-noise ratio (SNR) $<1$. Due to the flat sky assumption, Limber approximation and to avoid nonlinear effects, we have set lower and upper limits on $l$ for different redshift tomography bins. The galaxy cross-power spectra of different tomographic bins with low amplitudes and small overlapping redshift ranges of $n_{\rm g}^i(z)$ are also removed.
• Figure 4: The weighting functions of the CSST weak lensing survey for the four tomographic bins.
• Figure 5: The theoretical curves and mock data of the shear angular power spectra for the CSST 3$\times$2pt analysis. The blue solid curves are from the fiducial theoretical models. The red data points show the mock data used. Due to the flat sky assumption and Limber approximation, we have set lower limit on $l$ for different redshift tomography bins.