Probing the cosmic web in Lyα emission over large scales: an intensity mapping forecast for DECaLS/BASS and DESI

ABSTRACT Being the most prominent H i line, Ly$\alpha$ permeates the cosmic web in emission. Despite its potential as a cosmological probe, its detection on large scales remains elusive. We present a new methodology to perform Ly$\alpha$ intensity mapping with broad-band optical images, by cross-correlating them with Ly$\alpha$ forest data using a custom one-parameter estimator. We also develop an analytical large-scale Ly$\alpha$ emission model with two parameters (average luminosity $\langle L_{\rm Ly\alpha } \rangle$ and bias $b_{\rm e}$) that respects observational constraints from quasar (QSO) luminosity functions. We compute a forecast for Dark Energy Camera Legacy Survey (DECaLS)/Beijing–Arizona Sky Survey (BASS) g-band images cross-correlated with Dark Energy Spectroscopic Instrument (DESI) Ly$\alpha$ forest data, setting guidelines for reducing images into Ly$\alpha$ intensity maps. Given the transversal scales of our cross-correlation (26.4 arcmin, $\sim$33 cMpc h−1), our study effectively integrates Ly$\alpha$ emission over all the cosmic volume inside the DESI footprint at $2.2 \lt z \lt 3.4$ (the g-band Ly$\alpha$ redshift range). Over the parameter space ($\langle L_{\rm Ly\alpha } \rangle$, $b_{\rm e}$) sampled by our forecast, we find a 3$\sigma$ of large-scale structure in Ly$\alpha$ likely, with a probability of detection of 23.95 per cent for DESI–DECaLS/BASS, and 54.93 per cent for a hypothetical DESI phase-II with twice as much Ly$\alpha$ QSOs. Without a detection, we derive upper bounds on $\langle L_{\rm Ly\alpha } \rangle$ competitive with optimistic literature estimates [$2.3 \pm 1 \times 10^{\rm 41}$ erg s−1 (cMpc$^3$)−1 for DESI, and $\sim$35 per cent lower for its hypothetical phase-II]. Extrapolation to the DESI-Rubin overlap shows that a detection of large-scale structure with Ly$\alpha$ intensity mapping using next-generation imaging surveys is certain. Such detection would allow constraining $\langle L_{\rm Ly\alpha } \rangle$, and explore the constraining power of Ly$\alpha$ intensity mapping as a cosmological probe.