  An observational program focused on the high redshift ($2<z<6$) Universe has
the opportunity to dramatically improve over upcoming LSS and CMB surveys on
measurements of both the standard cosmological model and its extensions. Using
a Fisher matrix formalism that builds upon recent advances in Lagrangian
perturbation theory, we forecast constraints for future spectroscopic and 21-cm
surveys on the standard cosmological model, curvature, neutrino mass,
relativistic species, primordial features, primordial non-Gaussianity,
dynamical dark energy, and gravitational slip. We compare these constraints
with those achievable by current or near-future surveys such as DESI and
Euclid, all under the same forecasting formalism, and compare our formalism
with traditional linear methods. Our Python code FishLSS $-$ used to calculate
the Fisher information of the full shape power spectrum, CMB lensing, the
cross-correlation of CMB lensing with galaxies, and combinations thereof $-$ is
publicly available.
