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.
