a: SFR vs.z and b: M_⋆vs.z scatter plots. The green dotted line in panel a shows the empirical SFR values by Speagle et al. (2014) for MS field galaxies (SFR_MS) with stellar mass log(M_⋆/M_⊙) = 10.6, which corresponds to the mean stellar mass for the LIRGs in our sample. c,d: molecular gas to stellar mass ratio as function of redshift; the two plots differ in terms of the adopted α_CO, as shown at the bottom right of the panels. The green dotted lines show the empirical values found by Tacconi et al. (2018) for MS field galaxies with a stellar mass log(M_⋆/M_⊙) = 10.6. The color code for the data points is given in panels a,b.