  We derive the evolution of the infrared (IR) luminosity function (LF) over
the last 4/5ths of cosmic time, using deep 24um and 70um imaging of the GOODS
North and South fields. We use an extraction technique based on prior source
positions at shorter wavelengths to build the 24 and 70um source catalogs. The
majority (93%) of the sources have a spectroscopic (39%) or a photometric
redshift (54%) and, in our redshift range of interest (i.e., 1.3<z<2.3) ~20% of
the sources have a spectroscopic redshifts. To extend our study to lower 70um
luminosities we perform a stacking analysis and we characterize the observed
L_24/(1+z) vs L_70/(1+z) correlation. Using spectral energy distribution
templates which best fit this correlation, we derive the IR luminosity of
sources from their 24 and 70 um fluxes. We then compute the IR LF at
z=1.55+/-0.25 and z=2.05+/-0.25. The redshift evolution of the IR LF from z=1.3
to z=2.3 is consistent with a luminosity evolution proportional to
(1+z)^1.0+/-0.9 combined with a density evolution proportional to
(1+z)^-1.1+/-1.5. At z~2, luminous IR galaxies (LIRGs: 10^11Lsun< LIR
<10^12Lsun) are still the main contributors to the total comoving IR luminosity
density (IR LD) of the Universe. At z~2, LIRGs and ultra-luminous IR galaxies
(ULIRGs: 10^12Lsun< LIR) account for ~49% and ~17% respectively of the total IR
LD of the Universe. Combined with previous results for galaxies at z<1.3 and
assuming a constant conversion between the IR luminosity and star-formation
rate (SFR) of a galaxy, we study the evolution of the SFR density of the
Universe from z=0 to z=2.3. We find that the SFR density of the Universe
strongly increased with redshift from z=0 to z=1.3, but is nearly constant at
higher redshift out to z=2.3. As part of the online material accompanying this
article, we present source catalogs at 24um and 70um for both the GOODS-North
and -South fields.
