  After the successful full-shape analyses of BOSS data using the Effective
Field Theory of Large-Scale Structure, we investigate what upcoming galaxy
surveys might achieve. We introduce a ``perturbativity prior" that ensures that
loop terms are as large as theoretically expected, which is effective in the
case of a large number of EFT parameters. After validating our technique by
comparison with already-performed analyses of BOSS data, we provide Fisher
forecasts using the one-loop prediction for power spectrum and bispectrum for
two benchmark surveys: DESI and MegaMapper. We find overall great improvements
on the cosmological parameters. In particular, we find that MegaMapper (DESI)
should obtain at least a 12$\sigma$ ($2\sigma$) evidence for non-vanishing
neutrino masses, bound the curvature $\Omega_k$ to 0.0012 (0.012), and
primordial inflationary non-Gaussianities as follows:
$f_{\text{NL}}^{\text{loc.}}$ to $\pm 0.26$ (3.3), $f_{\text{NL}}^{\text{eq.}}$
to $\pm16$ (92), $f_{\text{NL}}^{\text{orth.}}$ to $\pm 4.2$ (27). Such
measurements would provide much insight on the theory of Inflation. We
investigate the limiting factor of shot noise and ignorance of the EFT
parameters.
