Low-redshift 3D Lyman-{\alpha} Forest Correlations with China Space Station Telescope

While the Lyman-$\alpha$ (Ly$\alpha$) forest traces the large-scale matter distribution over a wide range of redshift, its three-dimensional (3D) clustering at $z < 2$ has not yet been measured. We investigate the prospects for measuring low-redshift Ly$\alpha$ correlations with the UV slitless spectroscopic instrument of the China Space Station Telescope (CSST). We construct mock CSST quasar spectra that reproduce the expected survey depth, spectral resolution and noise properties, and derive Ly$\alpha$ auto-correlation functions and cross-correlations with quasars (QSO) and emission-line galaxies (ELG) in the range $1.1 < z < 2.0$. We then interpret these three-dimensional correlation functions with a standard anisotropic redshift-space clustering model and obtain forecast constraints on the Ly$\alpha$ and tracer parameters. At an effective redshift $z_{\rm eff}=1.59$ (1.58 for ELGs), the Ly$\alpha$ bias parameters will be measured with a 10-30\% precision, depending on priors on other tracer's biases. We also forecast a marginal $2.5\sigma$ ($3.7\sigma$) detection of the BAO feature, corresponding to a $\sim$10\% (7\%) constraint on the isotropic BAO scale, from the combination of Ly$\alpha$ auto- and Ly$\alpha$-QSO (ELG) cross-correlations. These results show that CSST can provide the first three-dimensional characterization of the low-redshift Ly$\alpha$ forest and a complementary Ly$\alpha$-based BAO measurement at $z < 2$, helping to link galaxy clustering surveys with high-redshift Ly$\alpha$ forest studies.