Forecasts for WEAVE-QSO: 3D clustering and connectivity of critical points with Lyman-α tomography

The upcoming WEAVE-QSO survey will target a high density of quasars over a large area, enabling the reconstruction of the 3D density field through Lyman-α (Ly-α) tomography over unprecedented volumes smoothed on intermediate cosmological scales (≈ 16 Mpc h^-1). We produce mocks of the Ly-α forest using Ly-α Mass Association Scheme, and reconstruct the 3D density field between sightlines through Wiener filtering in a configuration compatible with the future WEAVE-QSO observations. The fidelity of the reconstruction is assessed by measuring one- and two-point statistics from the distribution of critical points in the cosmic web. In addition, initial Lagrangian statistics are predicted from the first principles, and measurements of the connectivity of the cosmic web are performed. The reconstruction captures well the expected features in the auto- and cross-correlations of the critical points. This remains true after a realistic noise is added to the synthetic spectra, even though sparsity of sightlines introduces systematics, especially in the cross-correlations of points with mixed signature. Specifically, the most striking clustering features involving filaments and walls could be measured with up to 4σ of significance with a WEAVE-QSO-like survey. Moreover, the connectivity of each peak identified in the reconstructed field is globally consistent with its counterpart in the original field, indicating that the reconstruction preserves the geometry of the density field not only statistically, but also locally. Hence, the critical points' relative positions within the tomographic reconstruction could be used as standard rulers for dark energy by WEAVE-QSO and similar surveys.