Cosmological Fisher forecasts for next-generation spectroscopic surveys

Next-generation spectroscopic surveys such as the MegaMapper, MUltiplexed Survey Telescope (MUST), MaunaKea Spectroscopic Explorer (MSE), and Wide Spectroscopic Telescope (WST) are foreseen to increase the number of galaxy/quasar redshifts by an order of magnitude, with hundred millions of spectra that will be measured at $z>2$. We perform a Fisher matrix analysis for these surveys on the baryonic acoustic oscillation (BAO), the redshift-space distortion (RSD) measurement, the non-Gaussianity amplitude $f_{\rm NL}$, and the total neutrino mass $M_\nu$. For BAO and RSD parameters, these surveys may achieve precision at sub-percent level (<0.5 per cent), representing an improvement of factor 10 w.r.t. the latest database. For NG, these surveys may reach an accuracy of $\sigma(f_{\rm NL})\sim 1$. They can also put a tight constraint on $M_\nu$ with $\sigma(M_\nu) \sim 0.02\,\rm eV$ if we do joint analysis with Planck and even $0.01\,\rm eV$ if combined with other data. In addition, we introduce a general survey model, to derive the cosmic volume and number density of tracers, given instrumental facilities and survey strategy. Using our Fisher formalism, we can explore (continuously) a wide range of survey observational parameters, and propose different survey strategies that optimise the cosmological constraints. Fixing the fibre number and survey duration, we show that the best strategy for $f_{\rm NL}$ and $M_\nu$ measurement is to observe large volumes, despite the noise increase. However, the strategy differs for the apparent magnitude limit. Finally, we prove that increasing the fibre number improves $M_{\nu}$ measurement but not significantly $f_{\rm NL}$.