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Combining CMB datasets with consistent foreground modelling

This paper presents a unified likelihood analysis combining Planck, ACT, and SPT data to demonstrate that while standard $\Lambda$ CDM parameters remain robust under varying foreground models, cosmological extensions and foreground parameters are significantly more sensitive to these assumptions, highlighting the critical need for consistent foreground modelling in future CMB surveys.

Original authors: M. Tristram, M. Douspis, A. Gorce, S. Henrot-Versillé, L. T. Hergt, S. Ilic, L. McBride, M. Muñoz-Echeverría, E. Pointecouteau, L. Salvati

Published 2026-04-24

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CC BY 4.0

Original authors: M. Tristram, M. Douspis, A. Gorce, S. Henrot-Versillé, L. T. Hergt, S. Ilic, L. McBride, M. Muñoz-Echeverría, E. Pointecouteau, L. Salvati

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, ancient radio station that has been broadcasting a static-filled signal since the moment of the Big Bang. This signal is called the Cosmic Microwave Background (CMB). It's the oldest light in existence, and if we can tune into it clearly, it tells us the fundamental secrets of how our universe was built, how big it is, and what it's made of.

However, trying to listen to this ancient broadcast is like trying to hear a whisper in a crowded, noisy room. The "room" is filled with static from our own galaxy (dust clouds), distant galaxies, and even the equipment we use to listen. This static is called foreground noise.

For years, different teams of scientists have been trying to tune into this signal using different "radios" (telescopes):

Planck: A space telescope that sees the whole sky but with lower resolution (like a wide-angle lens).
ACT and SPT: Ground-based telescopes in the desert and at the South Pole that see small patches of the sky in extreme high definition (like a telephoto lens).

The Problem: Speaking Different Languages

Previously, each team tried to clean up the static in their own way. The Planck team used one recipe to remove dust, while the ACT team used a different recipe. When scientists tried to combine their results, it was like trying to bake a cake using three different recipes for the flour, sugar, and eggs. The result was messy, and it was hard to know if the final taste was due to the ingredients (cosmology) or the recipe (how they cleaned the data).

The Solution: A Unified Kitchen

This paper presents a new, unified approach. The authors built a single, master recipe to clean the static from all three telescopes at the same time.

Think of it like a team of chefs working in one kitchen. Instead of each chef cleaning their own vegetables separately, they all put their vegetables in one giant bowl and wash them together using the same water and soap. This ensures that:

Consistency: They aren't accidentally washing away the "good stuff" (the real cosmic signal) or leaving behind different amounts of "bad stuff" (noise).
Better Cleaning: Because they have data from the whole sky (Planck) and the high-definition patches (ACT/SPT), they can figure out exactly what the static looks like and remove it much more effectively than any single team could alone.

What They Found

Once they cleaned the signal using this new "unified kitchen" method, they looked at the results:

The Big Picture is Stable: The basic rules of the universe (how much dark matter there is, how fast it's expanding) didn't change much, no matter how they tweaked the cleaning recipe. This gives scientists great confidence that their measurements of the universe's foundation are solid.
The "Extra" Details are Tricky: However, when they looked at more complex questions—like "How heavy are neutrinos?" (tiny subatomic particles) or "Is the universe curved?"—the answer depended heavily on how they cleaned the static.
- Analogy: Imagine trying to guess the weight of a feather by weighing it on a scale. If you don't clean the dust off the scale perfectly, your guess for the feather's weight will be way off. The paper shows that for these complex questions, the "dust" (foregrounds) is a major source of uncertainty.
Old Conflicts Resolved: Some previous studies suggested the universe might be curved or that there was "too much" gravitational lensing. With this new, cleaner, combined data, those weird anomalies mostly disappeared. The universe looks much more like the standard model predicted.

The Takeaway

This paper is a major step forward because it proves that we can combine data from space and ground telescopes without them fighting each other.

It teaches us that how we clean our data is just as important as the data itself. For the next generation of super-powerful telescopes (which will be even more sensitive), getting the "cleaning recipe" right will be the difference between discovering new physics and just seeing more noise.

In short: The authors didn't just listen to the universe's radio; they built a better noise-canceling system that lets us hear the cosmic whisper much more clearly than ever before.

1. Problem Statement

Current cosmological constraints rely on data from multiple Cosmic Microwave Background (CMB) experiments, specifically the Planck satellite, the Atacama Cosmology Telescope (ACT), and the South Pole Telescope (SPT). While these datasets are complementary (Planck covers large angular scales; ACT and SPT provide high-resolution small-scale data), combining them has historically been challenging due to:

Inconsistent Foreground Modelling: Each collaboration uses different templates and assumptions for astrophysical foregrounds (Galactic dust, Cosmic Infrared Background [CIB], Sunyaev-Zel'dovich effects, and radio sources).
Systematic Biases: Differing treatments of instrumental systematics and foreground residuals make joint likelihoods difficult to interpret and reduce the reliability of combined constraints.
Priors: Previous joint analyses often relied heavily on external priors for foreground parameters, potentially biasing cosmological results.

The paper addresses the need for a unified, coherent likelihood framework that models the CMB signal and foregrounds consistently across all datasets to minimize reliance on external priors and accurately quantify systematic uncertainties.

2. Methodology

The authors constructed a joint likelihood combining Planck PR4, ACT DR6, and SPT-3G D1 datasets.

Likelihood Construction:
- Large Scales ( $\ell < 30$ ): Uses component-separated maps and specific low- $\ell$ likelihoods (Commander for TT, LoLLiPoP for polarisation).
- Small Scales ( $\ell \gtrsim 30$ ): Uses a Gaussian approximation of frequency cross-spectra. The covariance matrix includes instrumental and cosmic variance, accounting for correlations between multipoles and cross-frequency spectra.
- Multipole Overlap: To avoid double-counting and correlations, the analysis restricts ACT data to multipoles above Planck's effective range (TT: >2000, TE: >1500, EE: >1000). SPT and Planck overlap is negligible (<5% sky).
Unified Sky Model:
- A single model ( $\hat{C}_\ell$ ) is fitted simultaneously to all datasets.
- Components: CMB signal, Galactic dust (T & P), CIB (T), Thermal (tSZ), Kinetic (kSZ), and tSZ $\times$ CIB correlation, and Radio sources (T & P).
- Consistency: Extragalactic foreground templates (CIB, tSZ, kSZ, tSZ $\times$ CIB) are shared across all experiments. Parameters are fitted globally rather than per experiment.
Instrumental Systematics:
- The model includes 48 nuisance parameters covering calibration, polarisation efficiency, super-sample lensing, aberration, bandpass shifts, beam uncertainties, and temperature-to-polarisation leakage.
- Bandpass uncertainties for ACT are explicitly sampled using shift parameters.
Marginalisation Strategy:
- The authors perform Bayesian Model Averaging by running chains with different foreground template choices (e.g., different power spectrum shapes for CIB, tSZ, kSZ) and concatenating them into a "pseudo-chain."
- This allows them to marginalise over the choice of foreground models, separating statistical uncertainty from modelling uncertainty.

3. Key Contributions

First Fully Joint Analysis: This is the first work to simultaneously analyse Planck, ACT, and SPT data within a single likelihood framework with consistent foreground and systematic modelling.
Foreground Marginalisation: The study explicitly quantifies the uncertainty introduced by the choice of foreground templates, moving beyond simple statistical errors to include systematic modelling errors.
Data-Driven Constraints: By combining datasets with complementary frequency coverage and resolution, the analysis relaxes or removes informative priors on foreground parameters (e.g., dust spectral indices, CIB amplitudes) that were previously required for single-dataset analyses.
Updated Cosmological Constraints: Provides updated constraints on $\Lambda$ CDM parameters and extensions using the latest data releases (Planck PR4, ACT DR6, SPT-3G D1).

4. Key Results

A. $\Lambda$ CDM Cosmological Parameters

Stability: The six standard $\Lambda$ CDM parameters ( $\Omega_b h^2, \Omega_c h^2, \theta_s, \tau, A_s, n_s$ ) exhibit remarkable stability. Marginalising over foreground models increases uncertainties by less than 5% (except for $n_s$ , which increases by 9%).
Precision Gains: Combining the datasets improves precision compared to Planck alone:
- $\Omega_b h^2$ : Uncertainty reduced by 50%.
- $\Omega_c h^2$ : Uncertainty reduced by 17%.
- $\theta_s$ : Uncertainty reduced by 22%.
Consistency: The datasets show excellent agreement. No significant tension exists between temperature and polarisation constraints.

B. Foreground Parameters

Sensitivity to Modelling: Unlike cosmological parameters, foreground amplitudes are highly sensitive to modelling assumptions.
- CIB Amplitude ( $A_{CIB}$ ): Uncertainty is dominated by foreground modelling (dispersion $\approx$ 2 $\times$ statistical error). The recovered value is $4.32 \pm 0.33 (\text{stat}) \pm 0.60 (\text{fg}) \, \mu\text{K}^2$ .
- tSZ Amplitude: $A_{tSZ} = 2.98 \pm 0.22 (\text{stat}) \pm 0.10 (\text{fg}) \, \mu\text{K}^2$ .
- kSZ Amplitude: Not detected; upper limit $A_{kSZ} < 2.79 \, \mu\text{K}^2$ (95% CL). The result is consistent with zero but varies significantly with tSZ and point-source modelling.
- Point Sources: The treatment of radio sources significantly impacts the CIB and kSZ recovery.

C. Extensions to $\Lambda$ CDM

The study tests four extensions, finding that foreground modelling uncertainties can increase error bars by up to 35% in the neutrino sector:

Lensing Amplitude ( $A_L$ ): $A_L = 1.063 \pm 0.033$ . No evidence for anomalous lensing ( $A_L > 1$ ); the tension seen in previous Planck-only analyses is resolved.
Neutrino Mass ( $\Sigma m_\nu$ ): Upper limit $\Sigma m_\nu < 0.181$ eV (95% CL). The combined analysis improves the bound by a factor of two over Planck alone.
Effective Number of Relativistic Species ( $N_{\text{eff}}$ ): $N_{\text{eff}} = 3.031 \pm 0.130$ . Consistent with the Standard Model ($3.044$). Previous downward shifts seen in PR3 analyses are resolved with PR4 and the joint likelihood.
Spatial Curvature ( $\Omega_K$ ): $\Omega_K = -0.0132^{+0.0066}_{-0.0056}$ . Consistent with a flat universe; no evidence for a closed universe.

5. Significance and Conclusion

Robustness: The paper demonstrates that a fully joint analysis of current CMB experiments is feasible and robust. Cosmological parameters are stable against variations in foreground modelling, validating the current $\Lambda$ CDM model.
Systematic Uncertainty: The study highlights that for extensions to $\Lambda$ CDM (like neutrino mass) and foreground astrophysics, the uncertainty in modelling assumptions is often larger than statistical noise.
Future Outlook: The framework developed here is essential for next-generation surveys (Simons Observatory, CMB-S4). As these experiments reach higher sensitivities, the accuracy of foreground modelling will become the limiting factor for cosmological inference. The authors emphasize the need for unified, multi-dataset frameworks to disentangle true cosmological signals from astrophysical and instrumental systematics.

In summary, this work establishes a new standard for CMB data analysis by proving that consistent foreground modelling across experiments yields tighter, more reliable cosmological constraints while accurately quantifying the systematic uncertainties inherent in astrophysical foregrounds.