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We present new empirical constraints on the evolution of $\rho_{\rm H_2}$,the cosmological mass density of molecular hydrogen, back to $z\approx2.5$. Weemploy a statistical approach measuring the average observed $850\mu{\rm m}$flux density of near-infrared selected galaxies as a function of redshift. Theredshift range considered corresponds to a span where the $850\mu{\rm m}$ bandprobes the Rayleigh-Jeans tail of thermal dust emission in the rest-frame, andcan therefore be used as an estimate of the mass of the interstellar medium(ISM). Our sample comprises of ${\approx}150,000$ galaxies in the UKIDSS-UDSfield with near-infrared magnitudes $K_{\rm AB}\leq25$ mag and photometricredshifts with corresponding probability distribution functions derived fromdeep 12-band photometry. With a sample approximately 2 orders of magnitudelarger than in previous works we significantly reduce statistical uncertaintieson $\rho_{\rm H_2}$ to $z\approx2.5$. Our measurements are in broad agreementwith recent direct estimates from blank field molecular gas surveys, findingthat the epoch of molecular gas coincides with the peak epoch of star formationwith $\rho_{\rm H_2}\approx2\times10^7\,{\rm M_\odot}\,{\rm Mpc^{-3}}$ at$z\approx2$. We demonstrate that $\rho_{\rm H_2}$ can be broadly modelled byinverting the star-formation rate density with a fixed or weakly evolvingstar-formation efficiency. This 'constant efficiency' model shows a similarevolution to our statistically derived $\rho_{\rm H_2}$, indicating that thedominant factor driving the peak star formation history at $z\approx2$ is alarger supply of molecular gas in galaxies rather than a significant evolutionof the star-formation rate efficiency within individual galaxies.

Cosmic evolution of the H2 mass density and the epoch of molecular gas