SPT-3G 2018 TT/TE/EE+lensing Spectra Overview

• The paper presents precision measurements of CMB TT, TE, EE, and lensing spectra using the SPT-3G 2018 data, providing enhanced constraints on neutrino mass and ΛCDM extensions.
• It details a robust methodology including high-pass filtering, Monte Carlo covariance construction, beam uncertainty propagation, and calibration against Planck data.
• The integration with external datasets like BAO, DES, and Pantheon+ refines cosmological parameter limits, offering a powerful cross-check on small-scale CMB analyses.

The SPT-3G 2018 TT/TE/EE+lensing spectra comprise precise measurements of the cosmic microwave background (CMB) temperature (TT), E-mode polarization (EE), temperature-polarization cross-spectrum (TE), and the CMB lensing potential power spectrum (φφ) from the South Pole Telescope third-generation camera (SPT-3G), as analyzed in the context of cosmological parameter constraints, particularly neutrino masses and ΛCDM model extensions. These spectra are foundational for combined analyses with Planck, BAO, and low-redshift probes, and represent a critical advance in ground-based CMB high-multipole science (Gorbunov et al., 22 Jan 2026).

1. Measurement Specifications and Data Ranges

The SPT-3G 2018 spectra are derived from ~1500 deg² of the “Main field.” The relevant multipole (ℓ) coverage and binning, as employed in the joint cosmological analyses, are:

Spectrum	ℓ Range	Bin Width (Δℓ)
TT	750 ≤ ℓ ≤ 3000	Not specified here
TE, EE	300 ≤ ℓ ≤ 3000	Not specified here
φφ	~100 ≤ ℓ ≤ 2000	Not specified here

The “candl” package, which implements the likelihood and provides all bandpowers, employs window functions and covariance matrices defined in public SPT-3G 2018 data releases. The band-power binning is described in (Balkenhol et al., 2024), with typical Δℓ = 50 for primary spectra and Δℓ = 100 for lensing.

Instrumental noise is at or below several μK·arcmin per channel, with full beam window functions available and beam uncertainty propagated to the covariance matrix. Detailed beam properties, noise characterization, and map-making procedure (including high-pass filtering and destriping) are documented in the original instrument and data-release papers. Covariance matrices are constructed using Monte Carlo simulations that include signal and noise realizations. No further mode-projection beyond standard ground and scan-synchronous removal is reported (Gorbunov et al., 22 Jan 2026, Balkenhol et al., 2024).

2. Data Processing and Analysis Pipeline

2.1 Map-Making and Calibration

The raw time-ordered data undergo high-pass filtering to remove atmospheric and ground pickup, subtraction of scan-synchronous templates, and weighting into maps. Absolute calibration is achieved through cross-spectra with Planck 2018 maps; polarization angle calibration uses astronomical sources. The data are binned into pseudo-Cℓ band powers, with debiasing of transfer functions performed using simulation-derived corrections.

2.2 Systematic Corrections

Key systematics addressed in the 2018 pipeline include:

• Point-source masking
• T-to-P leakage template subtraction
• Full propagation of beam uncertainty in covariance
• Foreground templates included with wide priors in downstream likelihoods

No significant internal inconsistencies with Planck low-ℓ TT or EE spectra were found, obviating the need for additional consistency cuts (Gorbunov et al., 22 Jan 2026).

2.3 Covariance and Filtering

The covariance construction in “candl” includes sample variance, instrument noise, mode–mode coupling from the survey mask, and all relevant cross-covariances (including between φφ and TT/TE/EE). These are loaded from the official SPT-3G release and used without further analytic cropping (Balkenhol et al., 2024).

3. Theoretical Modeling and Likelihood Construction

3.1 Likelihood Formalism

The TT/TE/EE+lensing likelihood is built as a Gaussian in the binned bandpowers:

$$L(d|\theta) \propto \exp\left[ -\frac{1}{2} (D^{\rm data} - D^{\rm th}(\theta))^T {\rm Cov}^{-1} (D^{\rm data} - D^{\rm th}(\theta)) \right]$$

where $D^{\rm th}(\theta)$ are the theory spectra computed for cosmological parameters $\theta$, and Cov is the full bandpower covariance matrix. This form is implemented for both primary spectra and lensing, with joint likelihoods formed by summing component log-likelihoods as provided by the “candl” package and Planck modules.

3.2 Parameter Dependencies and Neutrino Mass

The sum of neutrino masses, $\sum m_\nu$, enters theory spectra by affecting the linear transfer functions (altering radiation-matter equality, the early ISW effect, and damping tail) and suppressing small-scale matter power, impacting $C_\ell^{\phi\phi}$. Three degenerate massive neutrinos are assumed, and theory spectra are generated with CLASS for each parameter set (Gorbunov et al., 22 Jan 2026).

4. Integration with External Data Sets

Joint parameter inference is conducted by combining SPT-3G 2018 TT/TE/EE+$\phi\phi$ with Planck PR3/PR4 low/high-ℓ likelihoods, DESI DR2 BAO, Dark Energy Survey (DES) Y1 weak lensing, and Pantheon+ SNIa catalogs. The likelihood structure is:

$$\ln L_{\rm total} = \ln L_{\rm SPT-3G}(\ell \geq 300) + \ln L_{\rm Planck,low}(\ell<30) + \ln L_{\rm Planck,highTT}(30<\ell<756) + \ln L_{\rm SPT-3G,lens} + \ln L_{\rm Planck,PR4,lens}$$

Sampling is performed with Cobaya+CLASS (Gorbunov et al., 22 Jan 2026). Planck high-ℓ TE/EE is not used because SPT-3G provides superior TE/EE down to ℓ = 300.

5. Cosmological Constraints

5.1 SPT-3G 2018 Standalone and Combined Results

Key limits on $\sum m_\nu$ (all 95% CL) from joint chains are:

Data Combination	$\sum m_\nu$ Upper Limit (eV)
CMB (SPT-3G+Planck low/high ℓ+lensing)	0.45
CMB+DESI BAO	0.110
+DES Y1 WL	0.125
+Pantheon+ SNIa	0.138

Incorporating DES Y1 weak lensing and Pantheon+ SNIa yields a posterior mode near 0.05 eV, with a mild preference for $\sum m_\nu > 0$ (Gorbunov et al., 22 Jan 2026).

5.2 Comparison: 2018 vs. 2019–2020 (D1+MUSE)

Switching to the SPT-3G D1 data (2019–2020) and its updated analysis pipeline leads to tighter constraints:

Data Combination	$\sum m_\nu$ Upper Limit (eV)
CMB-D1 (SPT-3G D1 alone)	0.30
CMB-D1+DESI BAO	0.069
+Pantheon+ SNIa	0.075
+DES Y1 WL	0.082

Unlike in the 2018 chains, the D1-based $\sum m_\nu$ posteriors remain peaked at zero, indicating no preference for minimal nonzero neutrino mass once low-redshift complementary data are included. This difference may reflect pipeline or noise reductions inherent to the D1 update (Gorbunov et al., 22 Jan 2026).

6. Robustness, Systematics, and Contextual Significance

Foreground templates (e.g., tSZ, radio and IR point sources) are incorporated with wide priors; shifts in these priors alter the Hubble constant constraint $H_0$ by less than 0.2σ. No significant internal tensions between SPT-3G and Planck low-ℓ TT/EE spectra are found. Comparison of the SPT-3G 2018 and D1 data sets shows a notable shift in neutrino-mass sensitivity arising from changes in noise levels, multipole cuts, and lensing-pipeline methodology.

SPT-3G achieves lower noise at $\ell\gtrsim2000$ than Planck, and for $\ell\gtrsim2200$ has lower errors in TE/EE than ACT DR6, providing a powerful independent check of ΛCDM on small scales and competitive constraints on extensions such as neutrino mass (Camphuis et al., 25 Jun 2025).

A plausible implication is that ongoing pipeline upgrades and systematic error controls in ground-based high-resolution experiments have direct, substantial impacts on cosmological parameter constraints and the interpretation of joint-probe analyses.

7. Data Products, Analysis Tools, and Cross-Experiment Comparison

The SPT-3G 2018 spectra and covariance matrices, along with likelihood modules, are provided through the “candl” Python package (Balkenhol et al., 2024). “candl” enables differentiable and JAX-accelerated likelihood evaluations and includes utility functions for Fisher-matrix forecasting and parameter covariance analysis. This infrastructure permits direct joint analyses with Planck and other CMB datasets.

Figure 1 of (Gorbunov et al., 22 Jan 2026) visually contrasts the one-dimensional posteriors for $\sum m_\nu$ from SPT-3G 2018 and D1 pipelines against Planck/ACT reference limits. Tabulated band powers, full covariance matrices, and likelihood scripts are public, ensuring reproducibility and facilitating cross-experiment synergy.

The SPT-3G 2018 TT/TE/EE+lensing spectra thus represent a critical high-resolution, deep-field CMB dataset that advances constraints on fundamental parameters such as $\sum m_\nu$, while providing rich opportunities for methodological refinement and cross-validation within the global cosmological community (Gorbunov et al., 22 Jan 2026, Balkenhol et al., 2024, Camphuis et al., 25 Jun 2025).