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Infrared (IR) luminosity is fundamental to understanding the cosmic star formation history and active galactic nuclei (AGN) evolution, since their most intense stages are often obscured by dust. However, local IR luminosity function estimates today are still based on the  IRAS  survey in the 1980s, with wavelength coverage only up to 100 μm. The  AKARI  IR space telescope performed an all‐sky survey in six IR bands (9, 18, 65, 90, 140 and  160 μm ) with 3–10 times better sensitivity, covering the crucial far‐IR wavelengths across the peak of the dust emission. Combined with a better spatial resolution,  AKARI  can much more precisely measure the total infrared luminosity  ( L  TIR )  of individual galaxies, and thus, the total infrared luminosity density in the local Universe.  By fitting modern IR spectral energy distribution (SED) models, we have remeasured   L  TIR   of the  IRAS  Revised Bright Galaxy Sample, which is a complete sample of local galaxies with   S  60 μm  &gt; 5.24  Jy.  We present mid‐IR monochromatic luminosity  (ν L  ν )  to   L  TIR   correlations for  Spitzer  8 μ m,  AKARI  9 μ m,  IRAS  12 μ m,  WISE  12 μ m,  ISO  15 μ m,  AKARI  18 μ m,  WISE  22 μ m and  Spitzer  24 μ m filters. These measures of   L  MIR   are well correlated with   L  TIR  , with scatter in the range 13–44 per cent. The best‐fitting   L  MIR  ‐to‐  L  TIR   conversions provide us with estimates of   L  TIR   using only a single MIR band, in which several deep all‐sky surveys are becoming available such as  AKARI  MIR and  WISE .  Although we have found some overestimates of   L  TIR   by  IRAS  due to contaminating cirrus/sources, the resulting  AKARI  IR luminosity function (LF) agrees well with that from  IRAS . We integrate the LF weighted by   L  TIR   to obtain a cosmic IR luminosity density of  Ω TIR = (8.5 +1.5  −2.3 ) × 10 7   L ⊙   Mpc −3 , of which  7 ± 1  per cent is produced by luminous infrared galaxies (LIRGs)  ( L  TIR  &gt; 10 11   L ⊙ ) , and only 0.4 ± 0.1 per cent is from ultraluminous infrared galaxies (ULIRGs)  ( L  TIR  &gt; 10 12   L ⊙ )  in the local Universe, in stark contrast to high‐redshift results.  We separate the contributions from AGN and star‐forming galaxies (SFGs). The SFG IR LF shows a steep decline at the bright end. Combined with high‐redshift results from the  AKARI  NEP deep survey, these data show a strong evolution of  Ω SF  TIR ∝  (1 + z )  4.0±0.5   and  Ω AGN  TIR ∝  (1 + z )  4.4±0.4  . For  Ω AGN  TIR  , the ULIRG contribution exceeds that from LIRGs already by   z ∼ 1 . A rapid evolution in both  Ω AGN  TIR   and  Ω SFG  TIR   suggests the correlation between star formation and black hole accretion rate continues up to higher redshifts. We compare the evolution of  Ω AGN  TIR   to that of X‐ray luminosity density. The  Ω AGN  TIR /Ω X‐ ray    AGN   ratio shows a possible increase at   z  &gt; 1 , suggesting an increase of obscured AGN at   z  &gt; 1 .

Luminosity functions of local infrared galaxies with AKARI : implications for the cosmic star formation history and AGN evolution