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Measurement of gravitational lensing of the cosmic microwave background using SPT-3G 2018 data

Z. Pan et al.
Phys. Rev. D 108, 122005 – Published 12 December 2023

Abstract

We present a measurement of gravitational lensing over 1500deg2 of the Southern sky using SPT-3G temperature data at 95 GHz and 150 GHz taken in 2018. The lensing amplitude relative to a fiducial Planck 2018 Lambda cold dark matter (ΛCDM) cosmology is found to be 1.020±0.060, excluding instrumental and astrophysical systematic uncertainties. We conduct extensive systematic and null tests to check the robustness of the lensing measurements, and report a minimum-variance combined lensing power spectrum over angular multipoles of 50<L<2000, which we use to constrain cosmological models. When analyzed alone and jointly with primary cosmic microwave background (CMB) spectra within the ΛCDM model, our lensing amplitude measurements are consistent with measurements from SPT-SZ, SPTpol, ACT, and Planck. Incorporating loose priors on the baryon density and other parameters including uncertainties on a foreground bias template, we obtain a 1σ constraint on σ8Ωm0.25=0.595±0.026 using the SPT-3G 2018 lensing data alone, where σ8 is a common measure of the amplitude of structure today and Ωm is the matter density parameter. Combining SPT-3G 2018 lensing measurements with baryon acoustic oscillation (BAO) data, we derive parameter constraints of σ8=0.810±0.033, S8σ8(Ωm/0.3)0.5=0.836±0.039, and Hubble constant H0=68.81.6+1.3kms1Mpc1. Our preferred S8 value is higher by 1.6 to 1.8σ compared to cosmic shear measurements from DES-Y3, HSC-Y3, and KiDS-1000 at lower redshift and smaller scales. We combine our lensing data with CMB anisotropy measurements from both SPT-3G and Planck to constrain extensions of ΛCDM. Using CMB anisotropy and lensing measurements from SPT-3G only, we provide independent constraints on the spatial curvature of ΩK=0.0140.026+0.023 (95% C.L.) and the dark energy density of ΩΛ=0.7220.026+0.031 (68% C.L.). When combining SPT-3G lensing data with SPT-3G CMB anisotropy and BAO data, we find an upper limit on the sum of the neutrino masses of mν<0.30eV (95% C.L.). Due to the different combination of angular scales and sky area, this lensing analysis provides an independent check on lensing measurements by ACT and Planck.

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  • Received 22 August 2023
  • Accepted 31 October 2023

DOI:https://doi.org/10.1103/PhysRevD.108.122005

© 2023 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsParticles & Fields

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Vol. 108, Iss. 12 — 15 December 2023

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Images

  • Figure 1
    Figure 1

    Noise spectra of coadded temperature maps for the 95 GHz and 150 GHz frequency bands.

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  • Figure 2
    Figure 2

    Biases in the CMB lensing autospectrum. The solid black line denotes the fiducial CMB lensing power spectrum. The realization dependent NL0 and NL1 biases for our deepest lensing map, ϕ^T95T150 as representative noise levels, are shown in black dashed and dotted lines, respectively. The power spectrum of the mean field (MF) for ϕ^T95T150 is plotted in dash-dotted line. The absolute value of the expected mean foreground contamination to the minimum-variance combination (see Sec. 4d, negative bias) is shown by the solid gray line while the shaded gray areas denote the 1σ and 2σ scatter with respect to the mean calculated over 16 cutouts from the agora simulations.

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  • Figure 3
    Figure 3

    Lensing κ maps reconstructed from the SPT-3G 1500deg2 field data, smoothed by a 1-degree FWHM Gaussian to highlight the large-scale modes with higher S/N ratio. We have also multiplied the maps by the point source and cluster mask discussed in Sec. 2e. The three left panels show the lensing convergence map inferred from three independent frequency combinations; 95×95GHz, 95×150GHz, and 150×150GHz. The right-hand side shows a minimum-variance-combined CMB lensing convergence map reconstructed in this work using 95 GHz and 150 GHz data and projected to equatorial coordinates. The SPT-3G footprint covers approximately 1500deg2 of the southern sky. The background shows the Galactic dust map from Planck Commander in intensity plotted in a logarithmic color scale.

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  • Figure 4
    Figure 4

    Comparison of the MV lensing band powers reconstructed using temperature data at 95 GHz and 150 GHz (black boxes) against band powers from individual frequency combinations (colored points). The solid line is the lensing spectrum from the Planck 2018 best-fit ΛCDM model.

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  • Figure 5
    Figure 5

    Lensing power spectrum measurements from this work, SPT-SZ (O17), SPTpol (W19), POLARBEAR [24], BICEP/Keck [18], Planck [22], and ACT [3]. We also plot the lensing spectrum from the best-fit ΛCDM model to the 2018 Planck TT,TE,EE+lowE+lensing dataset (solid gray line) [34, 49].

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  • Figure 6
    Figure 6

    Results of the power spectrum consistency tests and curl null test for the minimum-variance lensing band powers formed by combining temperature data at 95 GHz and 150 GHz. The band powers and errors for the baseline analysis are displayed as boxes. The band powers obtained from the different analysis choices are plotted with different colors and are in agreement with the baseline results. Note that we do not subtract the fiducial foreground bias template from these band powers.

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  • Figure 7
    Figure 7

    Comparison of difference bandpowers (ΔCLκκ) between the baseline analysis and those where we vary a given analysis setting, scaled by the uncertainties of the respective ϕTT bandpowers. The error bars represent the standard deviations of the shifts for 340 simulations with the same analysis choice change. The shaded gray regions represent the 1σ bands of the ϕTT estimators.

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  • Figure 8
    Figure 8

    Left: Constraints in the Ωmσ8 plane from our SPT-3G CMB lensing measurements (filled blue contours). For comparison, we also include results from Planck PR4 lensing (red contours) as well as its combination with SPT-3G lensing data (yellow contours). The empty blue contours show the constraints combining our SPT-3G lensing likelihood with BAO data. The black filled contours representing the independent constraints derived from the Planck primary CMB power spectra are also found to be consistent with the CMB lensing measurements at lower redshifts. Right: Comparison of Ωmσ8 constraints across different SPT surveys.

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  • Figure 9
    Figure 9

    Marginalized σ8Ωm0.25 posterior across different SPT, Planck, and ACT CMB lensing measurements. The shaded dark and light gray regions denote respectively the 1 and 2σ statistical errors from Planck PR3 CMB temperature and polarization anisotropies.

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  • Figure 10
    Figure 10

    A comparison of the marginalized constraints on the Hubble constant H0, S8σ8Ωm/0.3, and σ8 (left to right) across different cosmological probes and surveys. The direct H0 measurement is taken from Murakami et al. [37], while the LSS-based constraint on S8 is taken from the reanalysis of the DES-Y3 (+ BAO) data of [40] presented in Madhavacheril et al. [72].

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  • Figure 11
    Figure 11

    Consistency check between direct and indirect CMB lensing measurements. The amount of lensing directly inferred from SPT-3G data (AL×ALϕϕ) is consistent with what is predicted by the best-fit ΛCDM cosmology as determined from primary CMB when the smearing effects (AL) are marginalized over. This holds for both Planck PR3 primary CMB (orange contours) as well as 2018 SPT-3G data (blue contours).

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  • Figure 12
    Figure 12

    Marginalized constraints on the sum of the neutrino masses mν when BAO and either Planck (upper panel) or SPT-3G (lower panel) CMB temperature and polarization power spectra are folded into the cosmological inference. In each panel, the red and black lines show the effect of including direct lensing measurements from SPT-3G and Planck, respectively. The corresponding light dashed lines show instead the constraint when we remove the lensing information in the primary CMB, i.e. we allow AL to vary. The expectations for minimal masses based on oscillation measurements in the normal (NH) and inverted (IH) hierarchies are denoted by the gray shaded band and the dotted vertical line, respectively.

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  • Figure 13
    Figure 13

    Constraints on curvature and the matter density parameter obtained from the analysis of Planck primary CMB, with scattered points color-coded according to their corresponding Hubble constant values. The orange and black solid lines show the constraints inferred by adding either the SPT-3G or Planck lensing datasets, respectively. The blue solid lines denote instead the constraints from Planck primary CMB combined with BAO data, and indicate consistency with a flat geometry. The constraints obtained from both 2018 SPT-3G primary CMB and lensing are highlighted in red.

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