Redshift evolution of dense-gas mass density between the present-day (black point). The blue and purple points show dense-gas mass density inferred using the far-IR LFs from Zavala et al. (2021, blue) and Gruppioni et al. (2020, purple), respectively. The z ≈ 0 point (black) is inferred using HCN/FIR ratio from Jiménez-Donaire et al. (2019). We also show the upper limit from Rybak et al. (2022). Orange line points shows the evolution of total molecular gas density ρ_mol from Walter et al. (2020, orange solid line). Grey dashed line shows the Walter et al. (2020) trend normalised to match ρ_dense at z = 0. The ρ_dense evolution is consistent with the redshift evolution of ρ_mol with a constant dense-gas fraction of ≈3.5%.