Beyond dark energy Fisher forecasts: How the Dark Energy Spectroscopic Instrument will constrain LCDM and quintessence models

We baseline with current cosmological observations to forecast the power of the Dark Energy Spectroscopic Instrument (DESI) in two ways: (1) the gain in constraining power of parameter combinations in the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, and (2) the reconstruction of quintessence models of dark energy. For the former task we use a recently developed formalism to extract the leading parameter combinations constrained by different combinations of cosmological survey data. For the latter, we perform a nonparametric reconstruction of quintessence using the effective field theory of dark energy. Using mock DESI observations of the Hubble parameter, angular diameter distance, and growth rate, we find that DESI will provide significant improvements over current datasets on $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ and quintessence constraints. Including DESI mocks in our $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ analysis improves constraints on ${\mathrm{\ensuremath{\Omega}}}_{m}$, ${H}_{0}$, and ${\ensuremath{\sigma}}_{8}$ by a factor of two, where the improvement results almost entirely from the angular diameter distance and growth of structure measurements. Our quintessence reconstruction suggests that DESI will considerably improve constraints on a range of quintessence properties, such as the reconstructed potential, scalar field excursion, and the dark energy equation of state. The angular diameter distance measurements are particularly constraining in the presence of a non-$\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ signal in which the potential cannot be accounted for by shifts in ${H}_{0}$ and ${\mathrm{\ensuremath{\Omega}}}_{m}$.