Towards constraining cosmological parameters with SPT-3G observations of 25% of the sky

Technical Summary: Constraining Cosmological Parameters with SPT-3G Ext-10k Observations

Problem and Motivation
The South Pole Telescope (SPT) with its third-generation camera, SPT-3G, is conducting a comprehensive survey of the Cosmic Microwave Background (CMB) across approximately 10,000 deg² (25% of the sky) in temperature and polarization at 95, 150, and 220 GHz. This dataset, termed "Ext-10k," is composed of 13 distinct observational fields (Main, Summer, and Wide fields) that exhibit unique characteristics regarding observation elevation, atmospheric contamination, Galactic foregrounds, and noise properties.

A critical methodological question arises: does analyzing these 13 fields independently (treating them as separate regions) result in a significant loss of cosmological information compared to treating the entire survey as a single, contiguous field? Specifically, does neglecting the correlations between pixels across different fields diminish constraining power, particularly for large angular scales? Furthermore, the survey aims to address current cosmological tensions, such as the Hubble tension, by constraining extended models like Early Dark Energy (EDE) and varying electron mass models.

Methodology
To address these questions, the authors developed a realistic temperature and polarization likelihood pipeline using the candl framework (JAX-friendly and fully differentiable) coupled with the CosmoPower emulator.

1. Analysis Strategies: The authors compared two analysis approaches:

   • Ext10kjoint: Treating the 13 fields as a single contiguous patch with a common apodized border.
   • Ext10ksep: Treating the 13 fields as separate regions, each with its own apodized border.
   • Ext10kFDsep (Full Depth): The most realistic scenario, treating the 13 fields separately but assigning each its specific noise level (Main, Summer, and Wide fields have distinct sensitivities).

2. Likelihood Construction:

   • The likelihood is based on binned power spectra (TT, TE, EE) with a bin width of $\Delta\ell = 50$ and a multipole range of $350 \leq \ell \leq 4000$.
   • Covariance matrices were calculated analytically using a narrow kernel approximation (NKA) to account for mode coupling introduced by the apodized masks.
   • The pipeline includes realistic noise curves, transfer functions (accounting for time-ordered data filtering), and foreground modeling (radio galaxies, dusty star-forming galaxies, Galactic dust, CIB, tSZ, and kSZ).
   • A mock lensing likelihood was also constructed for the Main, Summer, and Wide fields to forecast constraints on extended models.

3. Forecasting:

   • Fisher matrix formalism was used for strategy validation (comparing joint vs. separate analyses).
   • Markov Chain Monte Carlo (MCMC) methods (using Cobaya) were employed for full forecasts on $\Lambda$CDM and extended models (varying electron mass in flat/curved universes, and axion EDE).
   • Forecasts were performed both for SPT-3G Ext-10k alone and in combination with a mock Planck likelihood (replacing real Planck data with theory spectra to avoid double-counting while maintaining consistency).

Key Contributions

• Validation of Independent Field Analysis: The paper provides a rigorous validation that analyzing the 13 Ext-10k fields independently does not significantly degrade cosmological parameter constraints.
• Realistic Pipeline Development: The authors developed and publicly released a likelihood pipeline capable of handling complex, multi-field surveys with heterogeneous noise and foreground properties.
• Extended Model Forecasts: The work extends previous forecasting efforts (e.g., Ref. [11]) by incorporating full foreground marginalization and lensing reconstruction to constrain models specifically proposed to resolve the Hubble tension.

Results

1. Impact of Analysis Strategy:

   • Comparing the joint and separate analyses (assuming identical Wide-field noise levels), the loss of constraining power is minimal. The difference in parameter variance is approximately 5%, translating to a relative uncertainty increase of less than 3% on standard $\Lambda$CDM parameters.
   • The primary source of this minor loss is the reduction in sky fraction ($f_{sky}$) due to the additional apodized borders in the separate analysis (22.15% vs. 23.22%), rather than the loss of cross-field correlations.
   • The Figure of Merit (FoM) for the separate case is roughly 10% lower than the joint case, but this difference is negligible compared to the improvement over Planck.

2. $\Lambda$CDM Constraints:

   • SPT-3G Ext-10k TT/TE/EE alone constrains parameters like $H_0$, $\Omega_b h^2$, and $\Omega_c h^2$ with precision comparable to or better than Planck PR3.
   • Adding CMB lensing ($\phi\phi$) significantly tightens constraints, improving $H_0$ and $\Omega_c h^2$ uncertainties by more than 30%.
   • Combining Ext-10k with Planck data improves constraints on $H_0$ and $\Omega_b h^2$ by factors of 1.9 and 2.2, respectively, compared to Planck alone.

3. Extended Models:

   • Varying Electron Mass ($m_e$): SPT-3G Ext-10k alone improves the FoM for a varying electron mass model in a flat universe by a factor of 112 compared to Planck. When combined with Planck, this factor rises to 192. For a curved universe model, the improvement is a factor of 162 (SPT alone) and 552 (combined).
   • Early Dark Energy (EDE): The combination of SPT-3G Ext-10k and Planck improves the FoM for the axion EDE model by a factor of 88 compared to Planck alone.
   • The constraints on $H_0$ in the varying electron mass models are approximately two times tighter with SPT-3G Ext-10k than with Planck alone.

Significance and Claims
The paper claims that the Ext-10k survey represents a significant step forward in cosmological precision. By validating the strategy of analyzing fields independently, the authors confirm that the survey can fully leverage its heterogeneous data without sacrificing information. The results suggest that SPT-3G Ext-10k data, particularly when combined with Planck, will provide stringent constraints on cosmological parameters, offering a powerful tool to test and potentially resolve the Hubble tension through models like varying electron mass and Early Dark Energy. The authors note that while their simulations are realistic, they do not yet include all systematic effects (such as full polarization beam marginalization or lensing foregrounds) that will be present in the final real-data analysis, but the current forecasts establish the dataset's potential.

Note: The authors acknowledge a correction made during proofreading regarding the lensing covariance, which increased error bars by ~15% for $\Lambda$CDM and reduced the FoM for extended models by a factor of ~10 compared to earlier assumptions, but confirmed that the overall conclusions regarding the dataset's merit remain valid.