Reanalyzing DESI DR1: 2. Constraints on Dark Energy, Spatial Curvature, and Neutrino Masses

TL;DR

This paper reevaluates DESI DR1 using an EFT-based full-shape analysis to test extensions to $Λ$CDM, including nonzero spatial curvature, dynamical dark energy, and neutrino masses, by combining DESI FS with CMB and SN datasets. The authors add the power-spectrum hexadecapole and the bispectrum monopole, employing AP-reparameterized EFT priors to mitigate projection effects, and demonstrate substantial gains in constraining power. They report the strongest CMB-independent bound on the total neutrino mass, $M_ν<0.32$ eV, and show that FS data significantly tighten curvature constraints and improve the dark-energy FoM; with CMB data, FS further tightens $M_ν$ bounds and shifts $w_0,w_a$ toward ΛCDM values in several combinations. The results underscore the value of incorporating FS power spectra and bispectra in non-minimal cosmological analyses and provide a framework for robust, beyond-$Λ$CDM inferences from DESI data.

Abstract

We carry out an independent re-analysis of the Dark Energy Spectroscopic Instrument (DESI) public dataset, focusing on extensions to the standard cosmological model, $Λ$CDM. Utilizing the dataset and Effective Field Theory (EFT)-based pipeline described in Paper 1, we constrain cosmological models with massive neutrinos ($Λ$CDM+$M_ν$), spatial curvature ($oΛ$CDM), dynamical dark energy ($w_0w_a$CDM), and their combinations using the power spectrum and bispectrum of DESI galaxies and quasars. Our work also presents the first measurements of relevant non-minimal 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 $\approx30\%$ and $\approx20\%$ relative to the CMB+BAO and CMB+BAO+SNe results, respectively. Our FS likelihood also yields the strongest CMB-independent constraint on the total neutrino mass $M_ν<0.32\,{\rm eV}$, with the $30\%$ improvement due to the bispectrum. In combination with the CMB, we find a $14\%$ improvement assuming the $Λ$CDM+$M_ν$ model (yielding $M_ν<0.059\,{\rm eV}$), but this increases to $22\%$ when using non-minimal backgrounds: $M_ν<0.097\,{\rm eV}$ in $oΛ$CDM+$M_ν$ and $M_ν<0.13\,{\rm eV}$ in $w_0w_a$CDM+$M_ν$. 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 non-minimal cosmological models.

Figures (6)

• Figure 1: Spatial curvature: Two-dimensional posterior distributions in the $\Omega_{\rm K}-H_0$ plane in the $o\Lambda{\rm CDM}$ analyses. Left panel: The inclusion of the DESI data breaks the geometric degeneracy present in the CMB data and brings $\Omega_{\rm K}$ into better agreement with a flat universe. Right panel: The combined analyses of the CMB and DESI data show a mild preference for $\Omega_{\rm K}>0$, with a significance ranging from $1.9\sigma$ to $2.4\sigma$, depending on the dataset combination. Using the newer HiLLiPoP+LoLLiPoP likelihoods Tristram:2020wbiTristram:2023haj, based on the Planck PR4 maps, alleviates this deviation, yielding $\Omega_{\rm K}$ values consistent with zero within 95% CL.
• Figure 2: Dynamical Dark Energy: Two-dimensional posterior distributions in the $w_0-w_a$ plane ( left panel) and one-dimensional marginalized posteriors for $\Omega_m$ ( right panel), when fixing the background model to $w_0w_a{\rm CDM}$. We also show the $\Omega_m$ posterior from the official DESI analysis of the BAO DR2 data in the $\Lambda{\rm CDM}$ model (black dashed line) DESI:2025zgx. Corresponding results including various SNe datasets are shown in Fig. \ref{['fig:w0wa_sn']}. Left panel: The significance of the tension with $\Lambda{\rm CDM}$ ($w_0=-1$, $w_a=0$) estimated from the $\Delta\chi^2_{\rm MAP}$ values is $2.9\sigma$, $2.8\sigma$ and $2.9\sigma$ for the $\rm {\rm CMB}+{\rm BAO}$, $\rm {\rm CMB}+{\rm BAO}+P_\ell+B_0$ and $\rm {\rm CMB}+{\rm BAO}+P_\ell+B_0+Pantheon+$ analyses, respectively. Right panel: The addition of the DESI DR1 FS information shifts the $\Omega_m$ posterior towards lower values in a closer agreement with the DESI-only $\Lambda{\rm CDM}$ result.
• Figure 3: Dynamical Dark Energy: Two-dimensional marginalized constraints on $w_0$ and $w_a$ parameters in the $w_0w_a{\rm CDM}$ analyses of the ${\rm CMB}+{\rm BAO}+{\rm SN}$ (dashed) and $\rm {\rm CMB}+{\rm BAO}+{\rm SN}+P_\ell+B_0$ (solid) data for three different SN Ia samples. The addition of the DESI DR1 power spectrum ($P_\ell$) and bispectrum monopole ($B_0$) data considerably improves constraints on the dark energy parameters: the Figure of Merit (FoM) for $w_0$ and $w_a$ increases by factors of $1.19$, $1.17$, and $1.19$ upon adding the DESI DR1 FS information for combinations involving PantheonPlus, Union3, and DESY5, respectively.
• Figure 4: Massive neutrinos: 1D marginalized posterior distributions for the sum of neutrino masses from different datasets. Left panel: Constraints on $M_\nu$ obtained in a $\Lambda{\rm CDM}$ background using the DESI DR2 BAO measurements, further including the DESI DR1 power spectrum $P_\ell$ (blue) and the DESI DR1 bispectrum monopole $B_0$ (orange), together with CMB data either from the official plik data release (red) or from the newer HiLLiPoP+LoLLiPoP likelihoods (dot-dashed). Right panel: constraints on $M_\nu$ from the CMB+BAO (dashed) and $\rm {\rm CMB}+{\rm BAO}+P_\ell+B_0$ (solid) dataset combinations in the $\Lambda{\rm CDM}$ (red), $w_0w_a{\rm CDM}$ (blue) and $o\Lambda{\rm CDM}$ (red) backgrounds. The minimal masses for the normal and inverted mass ordering scenarios, corresponding respectively to $M_\nu\geq 0.059{\,\rm eV}$ and $M_\nu\geq 0.10{\,\rm eV}$, are shown by the vertical dashed lines and shaded regions.
• Figure 5: Projection Effects in $\bm{w_0w_a}$CDM: Cosmological parameter constraints estimated from the synthetic mock data generated with our pipeline in the $w_0w_a{\rm CDM}$ model. Results are presented for three data combinations: ${\rm CMB}+{\rm BAO}$ (blue), ${\rm CMB}+{\rm BAO}+P_\ell$ (orange) and ${\rm CMB}+{\rm BAO}+P_\ell+B_0$ (green). The dashed black contours show the posterior distributions from the ${\rm CMB}+{\rm BAO}+P_\ell+B_0$ analysis derived using the original EFT priors from desi1.