Top panel: total dust-corrected UV-derived SFR density as a function of lookback time from the visible multi object-spectrograph (VIMOS)-VLT deep survey (VVDS) Deep + Ultra-Deep sample from Cucciati et al. (2012) is illustrated as black open circles. The red curve corresponds to the best-fitting parametric form to the SFR density from Hopkins & Beacom (2006). Bottom panel: the data points have the same meaning as in Fig. 9. The green curves represent the prediction of ρ_H   I from Nagamine et al. (2004, green triple dot-dashed line), Tescari et al. (2009, green solid line), and Lagos et al. (2011, green dashed line). The gray curves correspond to the prediction of ρ_H2 from Bauermeister et al. (2010, solid gray line) and Lagos et al. (2011, gray dashed line). The solid red line illustrates the evolution of the stellar mass density build-up inferred from the star formation history by Hopkins & Beacom (2006).