The molecular gas content of normal galaxies at z > 4 is poorly constrained , because the commonly used molecular gas tracers become hard to detect at these redshifts .
We use the [ C ii ] 158 \mu m luminosity , recently proposed as a molecular gas tracer , to estimate the molecular gas content in a large sample of main-sequence star-forming galaxies at z = 4.4 - 5.9 , with a median stellar mass of 10 ^ { 9.7 } ~ { } M _ { \odot } , drawn from the ALMA Large Program to INvestigate [ C ii ] at Early times ( ALPINE ) survey .
The good agreement between molecular gas masses derived from [ C ii ] luminosities , dynamical masses , and rest-frame 850 \mu m luminosities , extrapolated from the rest-frame 158 \mu m continuum , supports [ C ii ] as a reliable tracer of molecular gas in our sample .
We find a continuous decline of the molecular gas depletion timescale from z = 0 to z = 5.9 , which reaches a mean value of ( 4.6 \pm 0.8 ) \times 10 ^ { 8 } yr at z \sim 5.5 , only a factor of 2 - 3 shorter than in present-day galaxies .
This suggests a mild enhancement of star formation efficiency toward high redshifts , unless the molecular gas fraction significantly increases .
Our estimates show that the rise in molecular gas fraction as reported previously , flattens off above z \sim 3.7 to achieve a mean value of 63 \% \pm 3 \% over z = 4.4 - 5.9 .
This redshift evolution of the gas fraction is in line with the one of the specific star formation rate .
We use multi-epoch abundance matching to follow the gas fraction evolution over cosmic time of progenitors of z = 0 Milky Way-like galaxies in \sim 10 ^ { 13 } ~ { } M _ { \odot } halos and of more massive z = 0 galaxies in \sim 10 ^ { 14 } ~ { } M _ { \odot } halos .
Interestingly , the former progenitors show a monotonic decrease of the gas fraction with cosmic time , while the latter show a constant gas fraction from z = 5.9 to z \sim 2 and a steep decrease at z \lesssim 2 .
We discuss three possible effects , namely outflows , halt of gas supplying , and over-efficient star formation , which may jointly contribute to the gas fraction plateau of the latter massive galaxies .