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Understanding the star formation rate (SFR) variability and how it depends on physical properties of galaxies is important for developing and testing the theory of galaxy formation. We investigate how statistical measurements of the extragalactic background light (EBL) can shed light on this topic and complement traditional methods based on observations of individual galaxies. Using semi-empirical models of galaxy evolution and SFR indicators sensitive to different star formation time-scales (e.g. H α and ultraviolet continuum luminosities), we show that the SFR variability, quantified by the joint probability distribution of the SFR indicators (i.e. the bivariate conditional luminosity function), can be characterized as a function of galaxy mass and redshift through the cross-correlation between deep, near-infrared maps of the EBL and galaxy distributions. As an example, we consider combining upcoming SPHEREx maps of the EBL with galaxy samples from Rubin Observatory Legacy Survey of Space and Time. We demonstrate that their cross-correlation over a sky fraction of fsky ∼ 0.5 can constrain the joint SFR indicator distribution at high significance up to z ∼ 2.5 for mass-complete samples of galaxies down to $M_{*}\sim 10^9\, {\rm M}_{\odot }$. These constraints not only allow models of different SFR variability to be distinguished, butmore »also provide unique opportunities to investigate physical mechanisms that require large number statistics such as environmental effects. The cross-correlations investigated illustrate the power of combining cosmological surveys to extract information inaccessible from each data set alone, while the large galaxy populations probed capture ensemble-averaged properties beyond the reach of targeted observations towards individual galaxies.

We forecast the prospects for cross-correlating future line intensity mapping (LIM) surveys with the current and future Ly-α forest measurements. Using large cosmological hydrodynamic simulations, we model the emission from the CO rotational transition in the CO Mapping Array Project LIM experiment at the 5-yr benchmark and the Ly-α forest absorption signal for extended Baryon Acoustic Oscillations (BOSS), Dark energy survey instrument (DESI), and Prime Focus multiplex Spectroscopy survey (PFS). We show that CO × Ly-α forest significantly enhances the detection signal-to-noise ratio (S/N) of CO, with up to $300{{\ \rm per\, cent}}$ improvement when correlated with the PFS Ly-α forest survey and a 50–75 per cent enhancement with the available eBOSS or the upcoming DESI observations. This is competitive with even CO × spectroscopic galaxy surveys. Furthermore, our study suggests that the clustering of CO emission is tightly constrained by CO × Ly-α forest due to the increased sensitivity and the simplicity of Ly-α absorption modelling. Foreground contamination or systematics are expected not to be shared between LIM and Ly-α forest observations, providing an unbiased inference. Ly-α forest will aid in detecting the first LIM signals. We also estimate that [C ii] × Ly-α forest measurements from Experiment for Cryogenic Large-Aperture Intensity Mapping and DESI/eBOSS should have a larger S/N than planned [C ii] × quasarmore »observations by about an order of magnitude.

The cross-correlation between the 21 cm field and the galaxy distribution is a potential probe of the Epoch of Reionization (EoR). The 21 cm signal traces neutral gas in the intergalactic medium and, on large spatial scales, this should be anticorrelated with the high-redshift galaxy distribution, which partly sources and tracks the ionized gas. In the near future, interferometers such as the Hydrogen Epoch of Reionization Array (HERA) are projected to provide extremely sensitive measurements of the 21 cm power spectrum. At the same time, the Nancy Grace Roman Space Telescope (Roman) will produce the most extensive catalog to date of bright galaxies from the EoR. Using seminumeric simulations of reionization, we explore the prospects for measuring the cross-power spectrum between the 21 cm and galaxy fields during the EoR. We forecast a 12σdetection between HERA and Roman, assuming an overlapping survey area of 500 deg², redshift uncertainties ofσ_z= 0.01 (as expected for the high-latitude spectroscopic survey of Lyα-emitting galaxies), and an effective Lyαemitter duty cycle off_LAE= 0.1. Thus the HERA–Roman cross-power spectrum may be used to help verify 21 cm detections from HERA. We find that the shot-noise in the galaxy distribution is a limiting factor for detection,more »and so supplemental observations using Roman should prioritize deeper observations, rather than covering a wider field of view. We have made a public GitHub repository containing key parts of the calculation, which accompanies this paper:https://github.com/plaplant/21cm_gal_cross_correlation.