Reanalyzing DESI DR1: 4. Percent-Level Cosmological Constraints from Combined Probes and Robust Evidence for the Normal Neutrino Mass Hierarchy

TL;DR

This paper reanalyzes DESI DR1 with a unified one-loop EFT framework for galaxy clustering and bispectrum, augmented by photometric clustering and CMB lensing cross-correlations. By leveraging a cobra-based decomposition, IR resummation, and thorough treatment of biases and systematics, the authors extract percent-level constraints on $H_0$, $Ω_m$, and $σ_8$, and obtain a pronounced bound on the sum of neutrino masses. In ΛCDM, they find $M_ν<0.057$ eV (95% CL), with stronger distinctions in $w_0w_a$CDM that still favor the normal hierarchy; dynamical dark energy is mildly preferred at low redshift, and the dark energy figure-of-merit improves notably with the full-shape data. The results demonstrate the power of combining three- and two-point DESI statistics with lensing cross-correlations to deliver robust cosmological inferences and motivate further extensions to more general cosmological models.

Abstract

We present cosmological parameters measurements from the full combination of DESI DR1 galaxy clustering data described with large-scale structure effective field theory. By incorporating additional datasets (photometric galaxies and CMB lensing cross-correlations) and extending the bispectrum likelihood to smaller scales using a consistent one-loop theory computation, we achieve substantial gains in constraining power relative to previous analyses. Combining with the latest DESI baryon acoustic oscillation data and using cosmic microwave background (CMB) priors on the power spectrum tilt and baryon density, we obtain tight constraints on the $Λ$CDM model, finding the Hubble constant $H_0=69.08\pm 0.37~\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, the matter density fraction $Ω_m=0.2973\pm 0.0050$, and the mass fluctuation amplitude $σ_8 = 0.815\pm 0.016$ (or the lensing parameter $S_8\equivσ_8\sqrt{Ω_m/0.3}=0.811\pm 0.016$), corresponding to $0.6\%$, $1.7\%$, and $2\%$ precision respectively. Adding the Pantheon+ supernova sample (SNe), we find a preference of $2.6σ$ for the $w_0w_a$ dynamical dark energy model from low-redshift data alone, which increases to $2.8σ$ when exchanging the SNe with Planck CMB data. Combining full-shape data with BAO, CMB, and SNe likelihoods, we improve the dark energy figure-of-merit by $18\%$ and bound the sum of the neutrino masses to $M_ν<0.057$ eV in $Λ$CDM and $M_ν<0.095$ eV in the $w_0w_a$ dynamical dark energy model (both at 95\% CL). This represents an improvement of $25\%$ over the background expansion constraints and the strongest bound on neutrino masses in $w_0w_a$CDM to date. Our results suggest that the preference for the normal ordering of neutrino mass states holds regardless of the cosmological background model, and is robust in light of tensions between cosmological datasets.

Figures (6)

• Figure 1: DESI Measurements: Upper panel: Three-dimensional power spectrum and bispectrum measurements for the spectroscopic DESI DR1 LRG3 sample at $z_{\rm eff}=0.92$. The bispectrum dataset includes bins with centers ranging from $\bar{k}_{\rm min}=0.0075\,h{\text{Mpc}}^{-1}$ to $\bar{k}_{\rm max}=0.15\,h{\text{Mpc}}^{-1}$ (as described in the text), and the quadrupole moment, $B_2$, is offset along the $y$-axis for better visibility. Middle panel: Bispectrum multipoles for squeezed ($\bar{k}_{\rm min} =0.0075\,h{\text{Mpc}}^{-1}$) and equilateral configurations. The measurements are offset horizontally for better visibility. Lower panel: Cross-spectrum between the spectroscopic DESI DR1 LRG3 sample and the Planck PR4 and ACT DR6 CMB lensing maps (left panel), as well as the auto-spectrum of photometric DESI pLRG4 galaxies at $z_{\rm eff}=0.91$ and their cross-correlation with the lensing maps (right panel). We increase the galaxy auto-spectrum errors by a factor of ten for better visibility. Poisson shot noise terms have been subtracted from all relevant observables.
• Figure 2: $\Lambda$CDM constraints: Posterior distributions for the $\Lambda$CDM parameters $\Omega_m$, $H_0$, $\sigma_8$ and $S_8$ obtained by combining the DESI DR2 BAO measurements with the following combinations of data: (1) the DESI DR1 redshift-space power spectrum $P_\ell$ and tree-level bispectrum $B_\ell^{\rm tree}$ (gray); (2) adding the cross-correlation between the DESI spectroscopic samples and the CMB lensing reconstruction obtained from Planck and ACT observations (green); (3) adding also the (non-overlapping) DESI photometric galaxy samples, both in auto-correlation and through their cross-correlations with lensing (blue); (4) further adding small-scale spectroscopic bispectrum data-points, using a one-loop model for the galaxy three-point function (orange). In all cases, we impose Planck priors on the primordial power spectrum tilt and the physical baryon density. For comparison, we show constraints obtained from the Planck 2018 CMB two-point function combined with the Planck PR4 and ACT DR6 lensing reconstructions (red). Marginalized constraints are given in Table \ref{['tab:main2']}. For $H_0$ and $\Omega_m$, our DESI constraints are comparable to those from the CMB. For the amplitude parameters, we find that the constraints sharpen significantly when we add lensing cross-correlations and the one-loop bispectrum.
• Figure 3: $\Lambda$CDM constraints from bispectrum analysis variants: We show results from the full combination of spectroscopic and photometric two-point functions $P_\ell+[C_\ell^{\kappa g }]^{\text{spec-z}}+[C_{\ell}^{g g },C_{\ell}^{\kappa g }]^{\text{photo-z}}$ (denoted "FS 2pt"), combined with the tree-level bispectrum likelihood at $k_{\rm max}^{B_\ell}=0.08~h{\text{Mpc}}^{-1}$ (blue), and the one-loop likelihood at $k_{\rm max}^{B_\ell}=0.16~h{\text{Mpc}}^{-1}$ (orange) and $k_{\rm max}^{B_\ell}=0.2~h{\text{Mpc}}^{-1}$ (purple). The constraints improve slightly when upgrading the bispectrum likelihood from tree-level to one-loop, at the fiducial choice of $k_{\rm max}^{B_\ell}=0.16~h{\text{Mpc}}^{-1}$. Increasing the maximum scale to $k_{\rm max}^{B_\ell}=0.2~h{\text{Mpc}}^{-1}$ does not greatly reduce the error-bars, but produces significant shifts of the posterior contours. This behavior is similar to that observed in previous simulation-based studies Bakx:2025pop, and implies that two-loop corrections become important in this regime.
• Figure 4: $w_0w_a$CDM parameter constraints.Left Panel: One- and two-dimensional posterior distributions of the dynamical dark energy parameters for various combinations of datasets, as indicated by the caption. Here FS refers to the combined DESI DR1 full-shape dataset, comprising three-dimensional galaxy power spectra and one-loop bispectra, photometric galaxy correlations, and cross-correlations of CMB lensing with photometric and spectroscopic samples. The results shown in orange use CMB priors on $\omega_b$ and $n_s$, and those in black represent the standard combination from DESI:2025zgx. Black short-dashed lines mark the cosmological constant values of the dark energy equation of state parameters $(w_0,w_a)=(-1,0)$. The EFT-based full-shape likelihood improves the dark energy figure of merit (given by the inverse area of the posterior in the $w_0-w_a$ plane) by $18\%$. Right Panel:$\Omega_m$ inference from the same data combinations.
• Figure 5: Neutrino mass constraints: We show results including various combinations of DESI datasets in conjunction with the CMB likelihood and that of the Pantheon+ supernovae sample. Solid lines show constraints assuming the $w_0w_a$CDM background, while the dashed lines represent the limits obtained under the $\Lambda$CDM model. Marginalized constraints are given in Table \ref{['tab:mnu']}. Importantly, we find $\approx 25\%$ tighter constraints when combining the geometric BAO, CMB, and SNe probes (red) with the full-shape clustering statistics considered in this work. The combined neutrino mass constraints are in mild tension with the inverted hierarchy (rightmost vertical line) in both $\Lambda$CDM and $w_0w_a$CDM cosmological models.