We carry out an independent reanalysis of the dark energy spectroscopic instrument (DESI) public dataset, focusing on extensions to the standard cosmological model, $\mathrm{\Lambda }\mathrm{CDM}$. Utilizing the dataset and effective field theory-based pipeline described in Paper 1, we constrain cosmological models with massive neutrinos ($\mathrm{\Lambda }\mathrm{CDM}+M_{\nu }$), spatial curvature ($o\mathrm{\Lambda }\mathrm{CDM}$), dynamical dark energy ($w_0{w}_a\mathrm{CDM}$), and their combinations using the power spectrum and bispectrum of DESI galaxies and quasars. Our work also presents the first measurements of relevant nonminimal cosmological parameters from the combination of cosmic microwave background (CMB) and DESI full-shape (FS) data, which are made possible thanks to carefully chosen priors on EFT parameters. We find that the addition the FS likelihood to DESI’s baryon acoustic oscillation (BAO) data improves the limits on the spatial curvature by a factor of two over the BAO only results, though the improvements are less significant with the CMB data. The dark energy equation of state figure of merit increases both with and without the supernovae data (SNe), by $\approx 30\%$ and $\approx 20\%$ relative to the $\mathrm{CMB}+\mathrm{BAO}$ and $\mathrm{CMB}+\mathrm{BAO}+\mathrm{SNe}$ results, respectively. Our FS likelihood also yields the strongest CMB-independent constraint on the total neutrino mass $M_{\nu }<0.32\mathrm{eV}$, with the 30% improvement due to the bispectrum. In combination with the CMB, we find a 14% improvement assuming the $\mathrm{\Lambda }\mathrm{CDM}+M_{\nu }$ model (yielding $M_{\nu }<0.059\mathrm{eV}$), but this increases to 22% when using nonminimal backgrounds: $M_{\nu }<0.097\mathrm{eV}$ in $o\mathrm{\Lambda }\mathrm{CDM}+M_{\nu }$ and $M_{\nu }<0.13\mathrm{eV}$ in $w_0{w}_a\mathrm{CDM}+M_{\nu }$. Overall, our work illustrates that robust and substantial gains in constraining power can be obtained by incorporating the FS power spectrum and bispectrum measurements in analyses of nonminimal cosmological models.

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• Cosmological parameters
• Dark energy
• Large scale structure of the Universe
• Data analysis