  Today, thanks in particular to the results of the ESA Planck mission, the
concordance cosmological model appears to be the most robust to describe the
evolution and content of the Universe from its early to late times. It
summarizes the evolution of matter, made mainly of dark matter, from the
primordial fluctuations generated by inflation around $10^{-30}$ second after
the Big-Bang to galaxies and clusters of galaxies, 13.8 billion years later,
and the evolution of the expansion of space, with a relative slowdown in the
matter-dominated era and, since a few billion years, an acceleration powered by
dark energy. But we are far from knowing the pillars of this model which are
inflation, dark matter and dark energy. Comprehending these fundamental
questions requires a detailed mapping of our observable Universe over the whole
of cosmic time. The relic radiation provides the starting point and galaxies
draw the cosmic web. JAXA's LiteBIRD mission will map the beginning of our
Universe with a crucial test for inflation (its primordial gravity waves), and
the ESA Euclid mission will map the most recent half part, crucial for dark
energy. The mission concept, described in this White Paper, GAUSS, aims at
being a mission to fully map the cosmic web up to the reionization era, linking
early and late evolution, to tackle and disentangle the crucial degeneracies
persisting after the Euclid era between dark matter and inflation properties,
dark energy, structure growth and gravitation at large scale.
