To study the dust obscured phase of the galaxy evolution during the peak of the Star Formation Rate (SFR) and the Black Hole Accretion Rate (BHAR) density functions ($z = 1 - 4$), rest frame mid-to-far infrared (IR) spectroscopy is needed. At these frequencies, dust extinction is at its minimum and a variety of atomic and molecular transitions, tracing most astrophysical domains, occur. The future IR space telescope mission, SPICA, fully redesigned with its $2.5, rm{m}$ mirror cooled down to $T < 8, rm{K}$, will be able to perform such observations. With SPICA, we will: 1) obtain a direct spectroscopic measurement of the SFR and of the BHAR histories, 2) measure the evolution of metals and dust to establish the matter cycle in galaxies, 3) uncover the feedback and feeding mechanisms in large samples of distant galaxies, either AGN- or starburst-dominated, reaching lookback times of nearly 12 Gyr. SPICA large-area deep surveys will provide low-resolution, mid-IR spectra and continuum fluxes for unbiased samples of tens of thousands of galaxies, and even the potential to uncover the youngest, most luminous galaxies in the first few hundred million years. In this talk a brief review of the scientific preparatory work that has been done in extragalactic astronomy by the SPICA Collaboration will be given.
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