  We use the SPace Infrared telescope for Cosmology and Astrophysics (SPICA)
project as a template to demonstrate how deep spectrophotometric surveys
covering large cosmological volumes over extended fields (1-15 square degrees)
with a mid-IR imaging spectrometer (17-36 micron) in conjunction with deep 70
micron photometry with a far-IR camera, at wavelengths which are not affected
by dust extinction can answer the most crucial questions in current galaxy
evolution studies. A SPICA-like mission will be able for the first time to
provide an unobscured three dimensional (3-D, i.e. x, y and redshift z) view of
galaxy evolution back to an age of the Universe of less than ~2 Gyrs, in the
mid-IR rest-frame. This survey strategy will produce a full census of the Star
formation Rate (SFR) in the Universe, using Polycyclic Aromatic Hydrocarbons
(PAH) bands and fine-structure ionic lines, reaching the characteristic knee of
the galaxy luminosity function, where the bulk of the population is
distributed, at any redshift up to z ~3.5. Deep follow-up pointed spectroscopic
observations with grating spectrometers { onboard the satellite}, across the
full IR spectral range (17-210 micron), would simultaneously measure Black Hole
Accretion Rate (BHAR), from high-ionization fine-structure lines, and SFR, from
PAH and low- to mid-ionization lines in thousands of galaxies from solar to low
metallicities, down to the knee of their luminosity functions. The analysis of
the resulting atlas of IR spectra will reveal the physical processes at play in
evolving galaxies across cosmic time, especially its heavily dust-embedded
phase during the activity peak at the cosmic noon (z ~1-3), through IR emission
lines and features that are insensitive to the dust obscuration.
