(Top left panel) Evolution of φ_knee and L_knee as a function of redshift. (Top right panel) Evolution of the comoving number density of “faint” galaxies (i.e., 10⁷ L_⊙ < L_IR < 10¹¹ L_⊙; black triangles), LIRGs (10¹¹ L_⊙ < L_IR < 10¹² L_⊙; orange diamonds) and ULIRGs (L_IR > 10¹² L_⊙; red stars). Green circles show the number density of galaxies which are above the PACS detection limit of our ultradeep sub-sample (i.e., >, defined in Fig. 9). The local reference is taken from Sanders et al. (2003). (Bottom left panel) Evolution of the total comoving IR energy density (black area) and the relative contribution of the “faint” galaxies (light blue area), LIRGs (orange area) and ULIRGs (red area). The black dot-dashed line shows the best fit of the total comoving IR energy density, i.e., defined by integrating the IR LFs best-fitting our data points (see dashed lines in Fig. 10). The green dashed line shows the best fit of the comoving IR energy density of galaxies which are above the PACS detection limit of our ultradeep sub-sample (i.e., >). Black circles represent the total comoving IR energy density inferred by Gruppioni et al. (2013). The right axis of the panel shows the evolution of the obscured SFR density assuming that SFR   [M_⊙  yr^-1]  = 10^-10 × L_IR  [L_⊙] for a Chabrier (2003) IMF. (Bottom right panel) Evolution of the comoving IR energy density. Areas are the same as in the bottom left panel. The dotted lines represents the unobscured SFR density of the Universe (i.e., not corrected for extinction; Cucciati et al. 2012). The red dashed line on a white background shows the total SFR density of the Universe, defined as the sum of the obscured and unobscured SFR densities. Yellow diamonds are a compilation of SFR density estimates from Hopkins & Beacom (2006). Green circles and squares are the total SFR density of the Universe and the contribution of ULIRGs estimated by Murphy et al. (2011) using deep MIPS-24 and -70 μm observations. Dark blue diamonds, stars and triangles are estimates from Casey et al. (2012) for all galaxies, LIRGs and ULIRGs, respectively, using SPIRE (i.e., submillimetre) observations. One has to keep in mind that even with our ultradeep PACS data we only constrain the IR LFs of galaxies down to L_IR = 10¹¹ L_⊙ at z ~ 1 and L_IR = 10¹² L_⊙ at z ~ 2, respectively. Therefore, number densities and IR LDs of galaxies below these limits rely upon extrapolations based on φ_knee and L_knee and a faint-end slope fixed at its z ~ 0 value. The redshift and luminosity ranges for which the inferred number densities and IR LDs rely upon these extrapolations are highlighted by dashed lines and striped regions, respectively. We note that these extrapolations are nevertheless corroborated by direct constraints based on deep MIPS-24 μm observations (see Fig. 11).