Validation of Fast Mocks Generation for CSST Photometric Survey

Weak lensing has become a powerful tool for probing the matter distribution in the Universe and constraining cosmological parameters. This paper aims to explore the fast mock generation pipeline to obtain the covariance matrix of the $3\times 2$pt analysis for the upcoming China Space Station Telescope (CSST). We adopt the $N_\mathrm{side}$ pipeline, which generates matter distribution with lognormal assumptions, to create full-sky galaxy mocks with certain two-point statistics. We also employ the Markov-Chain Monte Carlo simulation to test the accuracy of the covariance matrix from the mock-generated galaxy catalogue. Our work validates the accuracy of the $3\times 2$pt statistics in both spherical harmonic space and real space. The critical scale below which the fractional error of correlation exceeds 1$\%$ can decrease as the resolution parameter $N_\mathrm{side}$ increases. After excluding certain scales, the covariance matrix from the mock-generated galaxy catalogue can constrain the cosmological parameters with 0.1$\%$ accuracy. This work demonstrates the potential of $\texttt{GLASS}$ for real-space cosmological measurements and highlights the importance of discarding appropriate scales.