Low-redshift constraints on structure growth from CMB lensing tomography

TL;DR

This paper constrains late-time structure growth (z ≲ 0.3) by combining galaxy clustering from 2MPZ and WIxSC with Planck CMB lensing, using Hybrid Effective Field Theory (HEFT) to model galaxy bias. By fitting the projected galaxy auto-spectrum and galaxy–CMB lensing cross-spectrum, the authors infer the parameter combination $S_8=\sigma_8\sqrt{\Omega_m/0.3}$, obtaining $S_8=0.79\pm0.06$ when including a DESI BAO prior on $\Omega_m$, in broad agreement with Planck. Without the BAO prior, the data prefer $\Omega_m=0.245\pm0.024$, about $2.8\sigma$ below Planck, driven by the broadband shape of the galaxy auto-correlation and sensitive to HEFT template uncertainties. They reconstruct the low-redshift growth history, finding it compatible with Planck, and show that HEFT bias parameters align with coevolution relations, supporting the robustness of the HEFT framework for these data. These results highlight both the potential and limitations of low-z lensing tomography for testing growth and gravity on cosmological scales and point to improvements from higher-order statistics and future surveys.

Abstract

We present constraints on the amplitude of matter fluctuations from the clustering of galaxies and their cross-correlation with the gravitational lensing convergence of the cosmic microwave background (CMB), focusing on low redshifts ($z\lesssim0.3$), where potential deviations from a perfect cosmological constant dominating the growth of structure could be more prominent. Specifically, we make use of data from the 2MASS photometric survey (\tmpz) and the \wisc galaxy survey, in combination with CMB lensing data from \planck. Using a hybrid effective field theory (HEFT) approach to model galaxy bias we obtain constraints on the combination $S_8=σ_8\sqrt{Ω_m/0.3}$, where $σ_8$ is the amplitude of matter fluctuations, and $Ω_m$ is the non-relativistic matter fraction. Using a prior on $Ω_m$ based on the baryon acoustic oscillation measurements of DESI, we find $S_8=0.79\pm0.06$, in reasonable agreement with CMB constraints. We also find that, in the absence of this prior, the data favours a value of $Ω_m=0.245\pm0.024$, that is 2.8$σ$ lower than \planck. This result is driven by the broadband shape of the galaxy auto-correlation, and may be affected by theoretical uncertainties in the HEFT power spectrum templates. We further reconstruct the low-redshift growth history, finding it to be compatible with the \planck predictions, as well as existing constraints from lensing tomography. Finally, we study our constraints on the HEFT bias parameters of the galaxy samples studied, finding them to be in reasonable agreement with coevolution predictions.

Figures (11)

• Figure 1: Top: redshift distributions of the three galaxy samples considered in this analysis. The bootstrap uncertainties are shown in a darker shade. Bottom: sky masks for the galaxy tracers (yellow) and the CMB lensing convergence map (dark blue).
• Figure 2: Relative error in the galaxy power spectrum incurred when extrapolating the dependence of the HEFT power spectrum templates on cosmological parameters. The red and blue lines show the result of extrapolating in $\sigma_8$ and $\Omega_m$, respectively. For guidance, the gray bands mark the limits where relative variations would exceed 1% and 2%. The start and end points of the extrapolation in each parameter are shown in the legend. Solid and dashed lines show results at $z=0.06$ and $0.39$, respectively.
• Figure 3: Power spectrum measurements and best-fit theory predictions. Each column displays the galaxy auto-correlation $C^{gg}_\ell$ (top) and the cross-correlation with CMB lensing $C^{g\kappa}_\ell$ (bottom), with the results for Bins 1, 2, and 3 (left, center, right). The sub-panel in each figure shows the difference between the data and the fiducial best-fit model (shown as a solid line in the main panels) as a fraction of the statistical uncertainties. The shaded bands show the angular scales excluded from the analysis.
• Figure 4: Two-dimensional constraints in the $(\Omega_m,S_8)$ plane. Results are shown for our fiducial analysis, combining all redshift bins, with $\Omega_m$ as a free parameter (red contours) and imposing a BAO prior from DESI on $\Omega_m$ (yellow), which we compare to Planck (blue). The gray band shows the $\Omega_m$ range over which the baccoemu HEFT emulator has been trained.
• Figure 5: Constraints on $\Omega_m$, $S_8$ and $\sigma_8$ found for the different analysis choices explored here, as well as the Planck measurements. The numerical constraints in each case are shown in Table \ref{['tab:constraints_bestfit']}. The black points and error bars represent the mean and $68\%$ confidence intervals, the same statistics used to estimate the tension levels. The pink shapes represent the marginalised posterior distributions from the MCMC chains.