Cosmology From CMB Lensing and Delensed EE Power Spectra Using 2019-2020 SPT-3G Polarization Data

TL;DR

This work demonstrates that polarization data alone from the SPT-3G instrument, analyzed with the Marginal Unbiased Score Expansion (MUSE) method, can deliver state-of-the-art measurements of the CMB lensing power spectrum and the unlensed EE spectrum. The approach yields a high-significance lensing detection (38σ) and tight ΛCDM parameter constraints, including H0 ≈ 66.8 km/s/Mpc and S8 ≈ 0.850, with tensions relative to distance-ladder and some weak-lensing probes. By combining SPT with Planck/ACT and BAO data, the paper confirms ΛCDM consistency across datasets while exploring non-linear lensing effects (A_mod^CMB ≈ 1.60) and neutrino mass bounds (Σmν < 0.075 eV with BAO). Additionally, the analysis highlights subtle indications of excess lensing power when comparing reconstructed and lensed spectra, and emphasizes improved beam modeling as a key factor after unblinding. Overall, the study demonstrates the power of joint Bayesian inference for CMB polarization while outlining avenues for reducing systematics and leveraging larger future data sets.

Abstract

From CMB polarization data alone we reconstruct the CMB lensing power spectrum, comparable in overall constraining power to previous temperature-based reconstructions, and an unlensed E-mode power spectrum. The observations, taken in 2019 and 2020 with the South Pole Telescope (SPT) and the SPT-3G camera, cover 1500 deg$^2$ at 95, 150, and 220 GHz with arcminute resolution and roughly 4.9$μ$K-arcmin coadded noise in polarization. The power spectrum estimates, together with systematic parameter estimates and a joint covariance matrix, follow from a Bayesian analysis using the Marginal Unbiased Score Expansion (MUSE) method. The E-mode spectrum at $\ell>2000$ and lensing spectrum at $L>350$ are the most precise to date. Assuming the $Λ$CDM model, and using only these SPT data and priors on $τ$ and absolute calibration from Planck, we find $H_0=66.81\pm0.81$ km/s/Mpc, comparable in precision to the Planck determination and in 5.4$σ$ tension with the most precise $H_0$ inference derived via the distance ladder. We also find $S_8=0.850\pm0.017$, providing further independent evidence of a slight tension with low-redshift structure probes. The $Λ$CDM model provides a good simultaneous fit to the combined Planck, ACT, and SPT data, and thus passes a powerful test. Combining these CMB datasets with BAO observations, we find that the effective number of neutrino species, spatial curvature, and primordial helium fraction are consistent with standard model values, and that the 95% confidence upper limit on the neutrino mass sum is 0.075 eV. The SPT data are consistent with the somewhat weak preference for excess lensing power seen in Planck and ACT data relative to predictions of the $Λ$CDM model. We also detect at greater than 3$σ$ the influence of non-linear evolution in the CMB lensing power spectrum and discuss it in the context of the $S_8$ tension.(abridged)

Figures (24)

• Figure 1: Verification that our pipeline recovers unbiased bandpower and systematics parameters using 100 mock simulations. The colored lines are the average MUSE parameter estimates over simulations after subtracting the input simulation truth (in the final panel we also divide by the errorbars for one simulation due to the otherwise large dynamic range). The first two panels show $\phi\phi$ and unlensed $EE$ bandpower amplitude parameters (and also consider single-frequency runs) and the last panel groups together all the systematics parameters (see Sec. \ref{['sec:model_summary']} and App. \ref{['app:model']} for description of the systematics considered). The PTEs of the colored lines relative to the expected scatter and 2-tailed numbers of $\sigma$ are shown in the legends. To get the PTEs, we Monte Carlo sample the expected distribution of $\chi^2$ values, accounting both for the look-elsewhere effect of 4 tests (3 single-frequency runs and 1 all-frequency run) and the fact that we compute the expected scatter itself from 100 mocks. For reference, gray bands are the all-frequency 1 and $2\,\sigma$ errors (note that this is not the expected scatter of any of the lines, rather is a way to judge the size of any potential bias).
• Figure 2: Verification of the accuracy of the all-frequency MUSE covariance, $\Sigma_{\rm MUSE}$. (Top left) Comparison of the square root of the diagonal elements between the MUSE covariance, $\sigma_{\rm MUSE}\,{\equiv}\,\sqrt{}{\rm diag}(\Sigma_{\rm MUSE})$, and the empirical covariance from running the estimate on mock simulations. (Bottom left) The ratio of the two curves in the upper panel. The shaded band shows the 1 and $2\,\sigma$ standard error on $\sigma_{\rm empirical}$ from the 100 simulations used. These are expected to match for fully likelihood-dominated parameters, and do so for all parameters except the partially prior-dominated $A_{\rm cal}$ parameters. (Top and bottom right) Comparisons of the first and second off-diagonal elements of the MUSE and empirical correlation matrices. In this case, systematics are assumed fixed in the MUSE covariance, since they are fixed in the simulations.
• Figure 3: The posterior correlation matrix of $\phi\phi$ bandpowers, unlensed $EE$ bandpowers, and systematics parameters, given all-frequency data.
• Figure 4: Verification that our pipeline recovers unbiased cosmological parameters using 100 mock simulations. We infer $\Lambda$CDM parameters from each simulated all-frequency dataset, and plot the one-dimensional marginalized posteriors above as different colored lines for each simulation. The shaded gray region in each panel is the product over all posteriors, which should cover the simulation truth, denoted as vertical black lines. Note that the smaller scatter for $\tau$ is because this parameter is mainly constrained by our prior. Across the other 5 parameters, the shaded region is consistent with the input truth with significance equivalent to $1.1\,\sigma$, suggesting no detection of any bias at the level afforded by our 100 simulations.
• Figure 5: Spectra of null maps computed from various data splits divided by the expected $1\,\sigma$ scatter due to noise. Detector wafer and scan direction tests also have had a small expected contribution from signal leakage subtracted, and in $EE$ and $BB$ have been computed with the exact pixel and Fourier space masking used in the main results pipeline (indicated as "MUSE masking"; the other tests are not expected to depend significantly on masking). Legends give the PTE for each test without correcting for the look-elsewhere effect. The $2\,\sigma$ threshold when considering the look-elsewhere effect is a PTE$>0.07\,\%$ on any individual test, which is passed in all cases.