Reanalyzing DESI DR1: 1. $Λ$CDM Constraints from the Power Spectrum and Bispectrum

TL;DR

The paper performs an independent EFT-based full-shape reanalysis of DESI DR1, augmenting the official approach with the hexadecapole power spectrum and a bispectrum monopole, alongside a novel stochastic fiber-collision estimator. By combining full-shape data with DESI DR2 BAO and Planck CMB, it produces precise $Λ$CDM constraints that align with CMB results and improve parameter degeneracy breaking via the bispectrum. The methodology demonstrates the critical role of higher-order statistics in constraining $Ω_m$, $H_0$, and $σ_8$, and shows robustness against estimator choices and systematic treatments. The work sets the stage for future full-shape analyses of non-minimal cosmologies and additional clustering statistics with DESI-like surveys.

Abstract

We present the first independent re-analysis of the galaxy clustering data from DESI Data Release 1, utilizing an effective field theory full-shape model. We analyze the power spectra and bispectra of the public catalogs using a custom-built pipeline based on window-deconvolved quasi-optimal estimators, accounting for a number of systematic effects. Compared to the official collaboration analysis, we add the galaxy power spectrum hexadecapole and the bispectrum monopole, and also introduce a novel stochastic estimator for fiber collisions, which facilitates robust bispectrum analyses. As a first application, we perform a full-shape analysis of the DESI power spectra and bispectra in the context of the standard cosmological model, $Λ$CDM. Using external priors on the physical baryon density and the primordial power spectrum tilt, we constrain the matter density fraction to $Ω_m=0.284\pm 0.011$, the Hubble constant to $H_0=70.7\pm 1.1$ km/s/Mpc, and the mass fluctuation amplitude to $σ_8=0.811\pm 0.030$. The bispectrum sharpens constraints on $σ_8$ and $Ω_m$ by $\approx 10\%$ and shifts $Ω_m$ by $\approx 1σ$ towards the \textit{Planck} $Λ$CDM value. Combining our full-shape likelihood with the official DESI DR2 BAO measurements, cosmological parameters shift further towards the \textit{Planck} values, with $Ω_m=0.296\pm 0.007$, $H_0=68.8\pm 0.6$ km/s/Mpc, $σ_8=0.818\pm 0.029$ (with tighter constraints obtained in joint analyses). Similar results are obtained in a joint analysis with DR1 BAO, accounting for the cross-covariance. Finally, the bispectrum data improves measurements of quadratic bias parameters, which are consistent with predictions from halo occupation distribution models. Our work highlights the importance of higher-order statistics and sets the stage for upcoming full-shape analyses of non-minimal cosmological models.

Figures (15)

• Figure 1: Summary of Results: Projected constraints on the $\Omega_m$, $H_0$ and $\sigma_8$ parameters in the $\Lambda{\rm CDM}$ model, using the following data combinations: the DESI DR1 redshift-space power spectrum $P_\ell$ (green), adding the DESI DR1 bispectrum monopole $B_0$ (blue), and including the DESI DR2 BAO measurements (orange). We include a BBN prior on $\omega_b$ and a wide prior on $n_s$ in all cases. The power spectrum and bispectrum measurements are new to this work; for the BAO, we take the latest results from DESI DR2 DESI:2025zgx, assuming negligible cross-correlation with the DR1 dataset (as validated in Appendix \ref{['app:cross']}). Results obtained using DR1 BAO (including the cross-correlation) are presented in Appendix \ref{['app:joint-bao']}. For comparison we also show the Planck 2018 CMB constraints, including lensing reconstruction from both the Plancknpipe PR4 maps and ACT DR6 (red). The DESI contours, which are the main result of this work, show good agreement with the CMB, particularly when additional information such as the bispectrum and BAO are included. The numerical constraints are listed in Tab. \ref{['tab:main']}.
• Figure 2: DESI $\boldsymbol{P_\ell(k)}$: Power spectra for the six DESI chunks used in this work. Each panel shows the power spectrum monopole (red), quadrupole (blue), and hexadecapole (green), measured using the PolyBin3D code, as described in §\ref{['sec: pspec']}. We include an off-diagonal normalization matrix to approximately deconvolve the window function, which leads to somewhat larger scatter than for conventional windowed estimators, though with no loss of signal-to-noise. For visualization, we rescale the ELG2 and QSO results by a constant factor as shown in the title. The solid lines indicate the best-fit theoretical model, obtained from a joint analysis of the DESI power spectra and bispectra (§\ref{['sec: lcdm-results']}). Errorbars indicate the Gaussian errorbars, with corrections for systematic effects and Monte Carlo noise, as shown in Fig. \ref{['fig: pk-cov']} The light points and lines indicate the data without correcting for fiber-collision effects (noting that there is little change to the theory model since we use quasi-unwindowed estimators), and the shot-noise contribution is shown in dashed lines (which is too large to see for QSO). The bottom panels indicate the difference between data and theory, in units of the errorbars.
• Figure 3: $\boldsymbol{P_\ell(k)}$ Errorbars: Contributions to the power spectrum variances for each data chunk, including the raw Gaussian covariances (blue), corrections for Monte Carlo noise entering the theory matrix (red) and shot-noise (orange) estimators, and, for ELG2 and QSO, angular systematics. The total errorbar is shown in black. For visibility, we stack the three Legendre multipoles into one dimension, as indicated by the vertical dashed lines. In all cases, the errorbar is dominated by the Gaussian contribution, implying that our Monte Carlo estimates of the theory and bias terms are sufficiently converged.
• Figure 4: DESI $\boldsymbol{B_0(k_1,k_2,k_3)}$: Bispectra for each of the six DESI data chunks. The red points show the bispectrum monopoles measured using PolyBin3D, with the best-fit theory curve shown as a dark red solid line (obtained from a joint power spectrum and bispectrum analysis). As for the power spectrum, we use (approximately) window-deconvolved estimators, which lead to anticorrelations between neighboring bins and thus considerable scatter in the datapoints. The contributions from shot-noise and the fiber-collision corrections are shown in black and green respectively. In all cases, we compress the data to a single dimension, with largest scales on the left ($k=0.02h\,\mathrm{Mpc}^{-1}$) and smallest scales on the right ($k=0.08h\,\mathrm{Mpc}^{-1}$). The bottom panel shows the difference between data and theory, and we find excellent agreement in all cases.
• Figure 5: Bispectrum Fiber Collisions: The impact of fiber collisions on the bispectrum numerator (left) and the diagonal of the normalization matrix (right). The purple lines give the fiducial contributions from all triplets of galaxies, with the total fiber-collision contributions are shown in black. This is decomposed into contributions from one (red), two (blue) and three (green) angular cuts, which are computed stochastically, as discussed in §\ref{['subsubsec: bspec-fiber']}. We find a clear fiber-collision signal in the numerator at the $(10-20)\%$ level, which is dominated by the single- and double-collision terms. In contrast, the correction to the normalization is small and sourced almost entirely by the single-collision piece.