Snowmass2021 Cosmic Frontier White Paper: Cosmology and Fundamental
  Physics from the three-dimensional Large Scale Structure
  Advances in experimental techniques make it possible to map the high redshift
Universe in three dimensions at high fidelity in the near future. This will
increase the observed volume by many-fold, while providing unprecedented access
to very large scales, which hold key information about primordial physics.
Recently developed theoretical techniques, together with the smaller size of
non-linearities at high redshift, allow the reconstruction of an order of
magnitude more "primordial modes", and should improve our understanding of the
early Universe through measurements of primordial non-Gaussianity and features
in the primordial power spectrum. In addition to probing the first epoch of
accelerated expansion, such measurements can probe the Dark Energy density in
the dark matter domination era, tightly constraining broad classes of dynamical
Dark Energy models. The shape of the matter power spectrum itself has the
potential to detect sub-percent fractional amounts of Early Dark Energy to $z
\sim 10^5$, probing Dark Energy all the way to when the Universe was only a few
years old. The precision of these measurements, combined with CMB observations,
also has the promise of greatly improving our constraints on the effective
number of relativistic species, the masses of neutrinos, the amount of spatial
curvature and the gravitational slip. Studies of linear or quasi-linear
large-scale structure with redshift surveys and the CMB currently provide our
tightest constraints on cosmology and fundamental physics. Pushing the redshift
and volume frontier will provide guaranteed, significant improvements in the
state-of-the-art in a manner that is easy to forecast and optimize.
