Unified and consistent structure growth measurements from joint ACT, SPT and \textit{Planck} CMB lensing

TL;DR

This work presents the first joint CMB lensing analysis combining ACT DR6, Planck PR4, and SPT-3G M2PM to measure the growth of structure with unprecedented precision. By constructing a joint lensing likelihood and incorporating DESI BAO and Pantheon+ data, the authors constrain $S^{\mathrm{CMBL}}_8$, $\sigma_8$, and $H_0$ within $\Lambda$CDM, while placing tight limits on the neutrino mass sum $\sum m_\nu$; results are consistent with Planck/ACT primary CMB predictions. The analysis achieves a combined lensing S/N of 61 and provides the most precise CMB lensing power spectrum to date, demonstrating the power of multi-survey lensing for testing structure growth across redshifts $z \sim 0.9$–$5$. The public release of the joint lensing likelihood and MCMC chains enables reproducibility and paves the way for future joint analyses with upcoming CMB surveys (e.g., SO, CMB-S4).

Abstract

We present the tightest cosmic microwave background (CMB) lensing constraints to date on the growth of structure by combining CMB lensing measurements from the Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT) and \textit{Planck}. Each of these surveys individually provides lensing measurements with similarly high statistical power, achieving signal-to-noise ratios of approximately 40. The combined lensing bandpowers represent the most precise CMB lensing power spectrum measurement to date with a signal-to-noise ratio of 61 and an amplitude of $A_\mathrm{lens}^\mathrm{recon} = 1.025 \pm 0.017$ with respect to the theory prediction from the best-fit CMB \textit{Planck}-ACT cosmology. The bandpowers from all three lensing datasets, analyzed jointly, yield a $1.6\%$ measurement of the parameter combination $S_8^\mathrm{CMBL} \equiv σ_8\,(Ω_m/0.3)^{0.25} = 0.825^{+0.015}_{-0.013}$. Including Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation (BAO) data improves the constraint on the amplitude of matter fluctuations to $σ_8 = 0.829 \pm 0.009$ (a $1.1\%$ determination). When combining with uncalibrated supernovae from \texttt{Pantheon+}, we present a $4\%$ sound-horizon-independent estimate of $H_0=66.4\pm2.5\,\mathrm{km\,s^{-1}\,Mpc^{-1}} $. The joint lensing constraints on structure growth and present-day Hubble rate are fully consistent with a $Λ$CDM model fit to the primary CMB data from \textit{Planck} and ACT. While the precise upper limit is sensitive to the choice of data and underlying model assumptions, when varying the neutrino mass sum within the $Λ\mathrm{CDM}$ cosmological model, the combination of primary CMB, BAO and CMB lensing drives the probable upper limit for the mass sum towards lower values, comparable to the minimum mass prior required by neutrino oscillation experiments.

Figures (10)

• Figure 1: Mollweide projection showing the sky coverage of ACT DR6 (red), Planck (orange) and SPT-3G M2PM (blue). ACT DR6 covers $23\%$ of the sky, SPT-3G M2PM covers $3.5\%$ and they overlap across $2.1\%$ of the sky. Planck PR4 covers $67\%$ of the sky. The grayscale background is a Galactic dust map from Planck1502.01588.
• Figure 2: We present the combined lensing bandpowers from the three surveys in black. In the background we show the Planck lensing bandpowers from PR4 NPIPE analysis in orange, the ACT DR6 lensing potential power spectrum bandpowers in red, and the lensing bandpowers from SPT-3G M2PM in blue. The gray line shows the theory prediction from the best-fit cosmology of the CMB likelihood. Note that we have applied an additional $L^{1/2}$ scaling over that usually used to display bandpowers to enhance visually the small scales.
• Figure 3: Marginalized posteriors in the $\sigma_8$--$\Omega_m$ plane for ACT DR6 (red), Planck PR4 (orange), SPT-3G M2PM (blue) and APS (black) CMB lensing measurements. Filled contours in the background show lensing‐only results, except for the black filled contour which represents APS+BAO. Non-filled contours (outlined) show results when including BAO data, which further breaks degeneracies in structure growth. The purple contours show the CMB prediction for a $\Lambda$CDM model. Each data set is shown with their $68\%$ and $95\%$ confidence limits.
• Figure 4: Marginalized posteriors in the $\sigma_8$--$\Omega_m$ plane for APS CMB lensing + BAO (filled black) and the CMB prediction for a $\Lambda$CDM model (purple). Allowing the sum of the neutrino masses to vary results in the open contours. Each data set is shown with their $68\%$ and $95\%$ confidence limits.
• Figure 5: Hubble constant measurements for the combination of CMB lensing and BAO are in filled black contours. The blue open contours show constraints on $H_0$ inferred from the matter--radiation equality scale as opposed to the sound-horizon scale. The $H_0$ measurements with CMB lensing are consistent with the low expansion rate inferred from the CMB in purple. We also show the $68\%$ bands of the Cepheid-calibrated direct inference in gray and the TRGB-calibrated direct inference in yellow.