Cosmological constraints from the angular power spectrum and bispectrum of luminous red galaxies and CMB lensing

TL;DR

This work develops and applies a joint analysis of the angular power spectrum, bispectrum, and CMB lensing cross-correlation of photometric luminous red galaxies to infer cosmology with an EFT-based perturbative bias model. By validating on AbacusSummit simulations and employing emulators to accelerate theory predictions, the authors reliably recover $Ω_m$, $σ_8$, and the derived $S_8$ while achieving a 10–20% improvement when including the bispectrum. The results show mild tension with Planck, predominantly driven by the first redshift bin, and demonstrate significantly tighter constraints on higher-order galaxy bias parameters. The approach showcases the potential of combining projected 2- and 3-point statistics with lensing for robust cosmological inferences in current and upcoming imaging surveys.

Abstract

We study the projected clustering of photometric luminous red galaxies from the DESI Legacy Survey, combining their angular power spectrum, bispectrum, and cross-correlation with maps of the CMB lensing convergence from the Planck satellite. We employ a perturbative bias expansion in Eulerian space to describe the clustering of galaxies, modelling the power spectrum and bispectrum at one-loop and tree level, respectively. This allows us to use the power spectrum to self-consistently calibrate the perturbative bias parameters. We validate this model against an $N$-body simulation, and show that it can be used up to scales of at least $k_{\rm max}^P\simeq 0.2\,h{\rm Mpc}^{-1}$ and $k_{\rm max}^B\simeq 0.08\,h{\rm Mpc}^{-1}$, saturating the information recovered from the data. We obtain constraints on the amplitude of matter fluctuations $σ_8=0.761\pm 0.020$ and the non-relativistic matter fraction $Ω_m=0.307\pm 0.015$, as well as the combination $S_8\equivσ_8\sqrt{Ω_m/0.3}=0.769 \pm 0.020$. Including the galaxy bispectrum leads to a $10$-$20\%$ improvement on the cosmological constraints, which are also in good agreement with previous analyses of the same data, and in mild tension with Planck at the $\sim2.5σ$ level. This tension is largely present in the standard two-point function dataset, and the addition of the bispectrum increases it slightly, marginally shifting $σ_8$ downwards and $Ω_m$ upwards. Finally, using the bispectrum allows for a substantially more precise measurement of the bias parameters of this sample, which are in reasonable agreement with existing coevolution relations.

Figures (15)

• Figure 1: Redshift distribution and scale cuts.Left: redshift distribution for each tomographic bin used here (filled histograms). The distribution of the simulated AbacusSummit sample is shown as dashed lines. Right: multipole-wavenumber relation, in the Limber approximation, for the filtered bispectrum data. The gray horizontal line marks the fiducial scale cut used here for the F$^2$B measurements.
• Figure 2: Model performance in simulated data. Figure of Bias (FoB, top panel), and Figure of Merit (FoM, bottom panel) for the galaxy-galaxy and galaxy-$\kappa$ angular power spectra in each redshift bin, for the two cosmological parameters $\{\Omega_m,\sigma_8\}$, as a function of the small-scale cut $k_{\rm max}^P$. Note that the FoM is reported relative to its value for $k_{\rm max}^P=0.08\,h{\rm Mpc}^{-1}$, in order to show results from all bins on the same scale. The solid lines refer to the nonlinear bias model assumed in our fiducial analysis, while dashed lines refer to a simplistic linear bias model. While linear bias can only give unbiased cosmological results up to $k_{\rm max}^P=0.1~h~\mathrm{Mpc}^{-1}$, the nonlinear model can extend to $k_{\rm max}^P=0.3~h~\mathrm{Mpc}^{-1}$ (but without significant gains in terms of extracted information for $k_{\rm max}^P>0.2~h~\mathrm{Mpc}^{-1}$).
• Figure 3: Consistency with bispectrum scale cut on simulation data. Posterior constraints on the model parameters as a function of the small-scale cut used for the galaxy bispectrum $k_\mathrm{max}^{B}$. Results are shown for two redshift bins, $z_3$ and $z_4$ (left and right panels, respectively). Similar results are found for the first two redshift bins. The shaded coloured bands show the $68\%$ constraints on each parameter, with the gray band showing the constraints found when using only power spectrum data with $k_{\rm max}^P=0.08\,h{\rm Mpc}^{-1}$ (and $\ell_{\rm min}=29$). Vertical lines represent, incrementally, the high-$\ell$ bound of the different filters used.
• Figure 4: Constraints from the AbacusSummit simulated data.Left: posterior, for single and combined redshift bins, of the cosmological parameters in the combined $gg+g\kappa+ggg$ analysis. The dashed lines show the true cosmological parameters of the AbacusSummit simulation, while the yellow cross marks the best-fit parameters found using the data covariance in the likelihood. The solid purple contours how the constraints obtained from the combination of all redshift bins, with the dotted contours showing the constraints found from individual redshift bins, all using the data covariance. The constraints found using the simulation covariance (significantly smaller due to the larger sky area and lack of lensing reconstruction noise) are shown in pink. The true cosmological parameters are recovered in all cases with no significant bias. Right: posterior, for the highest redshift bin, showing the relevant degeneracies of $\sigma_8$ with the bias parameters with and without the 3-point information, using the data covariance. This shows how the 1D posterior for $\sigma_8$ is affected by the marginalization over the bias parameters, especially along the degeneracy with $b_2$, when new information is added.
• Figure 5: Power spectrum and F$^2$B measurements, and model fit. Measurements of $C_\ell^{gg}$, $C_\ell^{g\kappa}$, and $\Phi_{LL\ell}^{ggg}$ in the fourth redshift bin. Results are shown over the scales used in the analysis, with the F$^2$B measurements covering the first two filters (the corresponding scale ranges are shown in the legend). The red line shows the best-fit model found from the combination of all data shown here, while the blue line shows the prediction found by fitting only the two-point functions. The lower panel reports the residuals with respect to the best-fit model normalized by the statistical uncertainties.