The cosmic web's Lyman-$\alpha$ glow at $z \approx 2.5$; varying hydrodynamic models, dust, and wide-field, narrow-band imaging detection

The diffuse glow of the cosmic web in Lyman-$\alpha$ emission has long been predicted, yet remained elusive to direct wide field detection. We present theoretical calculations that, when compared with recent observations made using the Condor Array Telescope in New Mexico reported in Lanzetta et al. 2024, point to its discovery at $z \approx 2.5$. Synthetic Lyman-$\alpha$ surface brightness maps are constructed from five state-of-the-art hydrodynamic simulations (Illustris-TNG, SIMBA, EAGLE, CROCODILE, and Sherwood), incorporating dust attenuation, star formation, collisional excitation, and recombination physics. Our cosmic web Lyman-$\alpha$ surface brightness predictions are consistent with the UV excess detected at high significance in the recent deep, wide field, narrow-band imaging Condor data. The calculations presented here thus demonstrate that diffuse Lyman-$\alpha$ emission is observable with current (and next-generation) wide field low surface brightness facilities, opening the path to direct cartographic mapping of the cosmic web. These findings mark a turning point: for the first time, cosmology moves beyond inference from absorption and high-density peaks, into panoramic imaging of the faint intergalactic scaffolding that underpins structure formation in the Universe.