Mapping the molecular gas content of the universe is key to our understanding of the build-up of galaxies over cosmic time. Spectral line scans in deep fields, such as the Hubble Ultra Deep Field (HUDF), provide a unique view on the cold gas content out to high redshift. By conducting `spectroscopy-of-everything, these flux-limited observations are sensitive to the molecular gas in galaxies without preselection, revealing the cold gas content of galaxies that would not be selected in traditional studies. In order to capitalize on the molecular gas observations, knowledge about the physical conditions of the galaxies detected in molecular gas, such as their interstellar medium conditions, is key. Fortunately, deep surveys with integral-field spectrographs are providing an unprecedented view of the galaxy population, providing redshifts and measurements of restframe UV/optical lines for thousands of galaxies. We present the results from the synergy between the ALMA Spectroscopic Survey of the HUDF (ASPECS), with deep integral field spectroscopy from the MUSE HUDF survey and multi-wavelength data. We discuss the nature of the galaxies detected in molecular gas without preselection and their physical properties, such as star formation rate and metallicity. We show how the combination of ALMA and MUSE integral field spectroscopy can constrain the physical properties in galaxies located around the main sequence during the peak of galaxy formation.
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