New Compressed Gaussian Likelihood Method for Planck CMB Polarization Data Released
Cosmologists have developed and publicly released a compressed Gaussian likelihood approximation for the Planck satellite's low-multipole CMB polarization data, derived from the SRoll2 likelihood. The tool addresses a fundamental incompatibility between the non-Gaussian nature of low-ℓ CMB likelihoods and Fisher matrix analyses widely used in cosmological forecasting. This enables researchers to incorporate Planck's tightest constraints on the reionization optical depth τ into standard Gaussian-likelihood-based pipelines without complex variable transformations.
A team of cosmologists has constructed a compressed Gaussian likelihood for the Planck CMB low-ℓ E-mode polarization data, building on the SRoll2 likelihood, which currently provides the most precise constraint on the reionization optical depth τ. The core technical challenge addressed is that low-ℓ CMB TT and EE likelihoods are inherently non-Gaussian, making them incompatible with Fisher matrix methods that assume an analytic Gaussian χ² form. The authors demonstrate that the χ² of an offset log-normal likelihood becomes Gaussian when expressed in log-transformed power spectrum amplitudes, allowing it to serve as a proxy for a true Gaussian likelihood in Fisher analyses. The SRoll2 likelihood is then compressed into a small number of piecewise offset log-normal functions, validated through MCMC runs combined with Planck and ACT DR6 data, showing excellent agreement across all ΛCDM parameters and in extended cosmological models. Fisher matrix uncertainty estimates derived from the compressed likelihood are also shown to match full MCMC posteriors well. The resulting software package, planck-gaussian-lowl, is a lightweight Python tool that also incorporates a previously published compressed low-ℓ TT likelihood, and is freely available for community use. The work was submitted to arXiv in June 2026 and has not yet undergone formal peer review.
What's missing
The study is a preprint and has not yet been peer-reviewed. Key open questions include how the compressed likelihood performs under more exotic extensions beyond ΛCDM, and how the tool will be maintained or updated if future SRoll2 data releases occur.
What different sources said
- arXiv astro-phCenter
Compressed Gaussian likelihood for the Planck low-$\ell$ data
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