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

Mid-IR cosmological spectrophotometric surveys from space: Measuring AGN and star formation at the Cosmic Noon with a SPICA-like mission