  We propose a new mission called Space Project for Astrophysical and
Cosmological Exploration (SPACE) as part on the ESA long term planning Voyage
2050 programme. SPACE will study galaxy evolution at the earliest times, with
the key goals of charting the formation of the heavy elements, measuring the
evolution of the galaxy luminosity function, tracing the build-up of stellar
mass in galaxies over cosmic time, and finding the first super-massive black
holes (SMBHs) to form. The mission will exploit a unique region of the
parameter space, between the narrow ultra-deep surveys with HST and JWST, and
shallow wide-field surveys such as Roman Space Telescope and EUCLID, and should
yield by far the largest sample of any current or planned mission of very high
redshift galaxies at z > 10 which are sufficiently bright for detailed
follow-up spectroscopy. Crucially, we propose a wide-field spectroscopic
near-IR + mid-IR capability which will greatly enhance our understanding of the
first galaxies by detecting and identifying a statistical sample of the first
galaxies and the first SMBH, and to chart the metal enrichment history of
galaxies in the early Universe - potentially finding signatures of the very
first stars to form from metal-free primordial gas. The wide-field and
wavelength range of SPACE will also provide us a unique opportunity to study
star formation by performing a wide survey of the Milky Way in the near-IR +
mid-IR. This science project can be enabled either by a stand-alone ESA-led M
mission or by an instrument for an L mission (with ESA and/or NASA, JAXA and
other international space agencies) with a wide-field (sub-)millimetre
capability at wavelength > 500 microns.
