Atomic and molecular gas from the epoch of reionization down to redshift 2

Cosmic gas makes up about 90% of baryonic matter in the Universe and H$_2$ is the closest molecule to star formation. In this work we study cold neutral gas and its H$_2$ component at different epochs, exploiting state-of-the-art hydrodynamic simulations that include time-dependent atomic and molecular non-equilibrium chemistry coupled to star formation, feedback effects, different UV backgrounds presented in the recent literature and a number of additional processes - such as gas self-shielding, H$_2$ dust grain catalysis, photoelectric and cosmic-ray heating - occurring during structure formation (ColdSIM). We find neutral-gas mass density parameters $\Omega_{\rm neutral} \simeq$10$^{-3}$ and increasing from lower to higher redshift, in agreement with available HI data. Resulting H$_2$ fractions can be as high as $\sim$50% at $z\sim$4-8, in line with the latest high-$z$ measurements. Albeit dependent on the adopted UV background, derived $\Omega_{\rm H_2}$ values agree with observations up to $z\sim$7 and both HI and H$_2$ trends are better reproduced by our non-equilibrium H$_2$-based star formation modelling. The predicted gas depletion timescales decrease towards lower $z$, with H$_2$ depletion times remaining below the Hubble time and comparable to the dynamical time at all considered redshifts. This implies that non-equilibrium molecular cooling is efficient at driving cold-gas collapse in a broad variety of environments and since the very early cosmic epochs. In appendix, we show detailed analyses of individual processes, as well as simple numerical parameterizations and fits to account for them. Our findings suggest that, in addition to HI, non-equilibrium H$_2$ observations are pivotal probes for assessing cold-gas abundances and the role of UV background radiation - Abridged