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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. [ABSTRACT FROM AUTHOR]

The D4000 spectral break index is one of the most important features in the visible spectrum, as it is a proxy for stellar ages and is also used in galaxy classification. However, its direct measurement has always been reserved to spectroscopy. Here, we present a general method to directly measure the D4000 with narrow-band (NB) photometry; it has been validated using realistic simulations, and then evaluated with PAUS NBs, cross-matched with VIPERS spectra (i AB < 22.5, 0.562 < z < 0.967). We also reconstruct the D4000 with the SED-fitting code cigale ; the use of PAUS NBs instead of broad-bands significantly improves the SED fitting results. For D4000n, the direct measurement has |$\rm \langle SNR \rangle \sim 4$|⁠ , but we find that for i AB < 21 all direct D4000 measurements have |$\rm SNR\gt 3$|⁠. The cigale D4000n has |$\rm \langle SNR \rangle \sim 20$|⁠ , but underestimates the error by >50 per cent. Furthermore, the direct method recreates well the D4000–SFR relation, as well as the D4000–mass relation for blue galaxies (for red galaxies, selection effects impact the results). On the other hand, cigale accurately classifies galaxies into red and blue populations. We conclude that the direct measurement of D4000 with narrow-band photometry is a promising tool to determine average properties of galaxy samples, with results compatible with spectroscopy. [ABSTRACT FROM AUTHOR]