Stars were born in significantly denser regions in the early Universe

The density of the warm ionized gas in high-redshift galaxies is known to be higher than what is typical in local galaxies on similar scales. At the same time, the mean global properties of the high- and low-redshift galaxies are quite different. Here, we present a detailed differential analysis of the ionization parameters of 14 star-forming galaxies at redshift 2.6-3.4, compiled from the literature. For each of those high-redshift galaxies, we construct a comparison sample of low-redshift galaxies closely matched in specific star formation rate (sSFR) and stellar mass, thus ensuring that their global physical conditions are similar to the high-redshift galaxy. We find that the median log [OIII] 5007/ [OII] 3727 line ratio of the high-redshift galaxies is 0.5 dex higher than their local counterparts. We construct a new calibration between the [OIII] 5007/ [OII] 3727 emission line ratio and ionization parameter to estimate the difference between the ionization parameters in the high and low-redshift samples. Using this, we show that the typical density of the warm ionized gas in star-forming regions decreases by a median factor of $7.1^{+10.2}_{-5.4}$ from z ~ 3.3 to z ~ 0 at fixed mass and sSFR. We show that metallicity differences cannot explain the observed density differences. Because the high- and low-redshift samples are comparable in size, we infer that the relationship between star formation rate density and gas density must have been significantly less efficient at z ~2-3 than what is observed in nearby galaxies with similar levels of star formation activity.