Unveiling the evolution of the CO excitation ladder through cross-correlation of CONCERTO-like experiments and galaxy redshift surveys

Context. While acting as a foreground for [CII] line intensity mapping (LIM) experiments, rotational CO transitions serve as valuable indicators of the physical conditions of cold gas in the interstellar media of galaxies at lower redshifts. It is also essential to study these transitions to enhance component separation methods as LIM experiments improve in sensitivity. Aims. Until now, galaxy-evolution models have been used to predict the total LIM CO signal across all transitions. This study investigates the potential of cross-correlating millimeter-wave LIM data with spectroscopic galaxy surveys to constrain individual CO line contributions. We aim to measure the CO-background spectral-line energy distribution (SLED) and the cosmic molecular gas density ρH2(z) up to z = 3. Methods. We constructed 12 light cones of 9-deg2 from the Simulated Infrared Extragalactic Sky (SIDES) simulation. By analyzing the amplitude ratios of the cross-power spectra between various CO transitions and the galaxy density field, we recovered the CO background SLED. We then combined the derived SLED with the bias-weighted line intensities to estimate ρH2(z). Finally, we assess the feasibility of measuring the CO(4–3) cross-power spectra with a CONCERTO-like experiment. Results. Using a realistic depth for a spectroscopic survey, this work accurately recovers the CO background SLED up to Jup = 6, with uncertainties ≤20%. Then, reconstructing ρH2, from millimeter-LIM experiments requires introducing an excitation correction relative to CO(1–0). We demonstrate that interloper-induced variance does not prevent precise estimation of ρH2. Using the two-star-formation-mode model of SIDES, we show that starbursts contribute significantly to the SLED at Jup ≥ 6, but they do not significantly bias the estimation of ρH2 from upper 2 ≤ Jup ≤ 6 transitions. However, CONCERTO lacks the sensitivity to detect the CO × galaxy cross-power at relevant scales, even under ideal survey conditions.