  We illustrate the extraordinary discovery potential for extragalactic
astrophysics of a far-IR/submm all-sky spectroscopic survey with a 3m-class
space telescope. Spectroscopy provides both a 3D view of the Universe and
allows us to take full advantage of the sensitivity of present-day
instrumentation, overcoming the spatial confusion that affects broadband
far-IR/submm surveys. Emission lines powered by star formation will be detected
in galaxies out to $z \simeq 8$. It will provide measurements of spectroscopic
redshifts, SFRs, dust masses, and metal content for millions of galaxies at the
peak epoch of cosmic star formation and of hundreds of them at the epoch of
reionization. Many of these galaxies will be strongly lensed; the brightness
amplification and stretching of their sizes will make it possible to
investigate (by means of follow-up with high-resolution instruments) their
internal structure and dynamics on the scales of giant molecular clouds. This
will provide direct information on the physics driving the evolution.
Furthermore, the arc-min resolution of the telescope at submm wavelengths is
ideal for detecting the cores of galaxy proto-clusters, out to the epoch of
reionization. Tens of millions of these galaxy-clusters-in-formation will be
detected at $z \simeq 2$-3, with a tail out to $z \simeq 7$, and thousands of
detections at 6 < z < 7. Their study will allow us to track the growth of the
most massive halos well beyond what is possible with classical cluster surveys
(mostly limited to $z < 1.5$-2), tracing the history of star formation in dense
environments and teaching us how star formation and galaxy-cluster formation
are related across all epochs. Such a survey will overcome the current lack of
spectroscopic redshifts of dusty star-forming galaxies and galaxy
proto-clusters, representing a quantum leap in far-IR/submm extragalactic
astrophysics.
