Top: redshift evolution of the molecular gas mass density based on Eq. (1). Red symbols and solid error bars belong to the total mass density, dashed error bars mark lower limits limited to the mass range covered by observations. The black star is computed by integrating the local mass function (Keres et al. 2003). Gray squares and triangles represent the total M _⋆  density reported by Ilbert et al. (2013) and Muzzin et al. (2013), respectively. Light-blue symbols belong to star-forming galaxies only. Bottom: evolution of Ω_mol (red symbols, this work) and Ω_HI (Prochaska & Herbert-Fort 2004; Zwaan et al. 2005; Rao et al. 2006), where we have divided the latter by 1.3 to avoid counting helium twice.