$ exttt{unimpeded}$: A Public Grid of Nested Sampling Chains for Cosmological Model Comparison and Tension Analysis

Modern cosmology relies heavily on Bayesian inference to test theoretical models against observational data, but the computational cost of these analyses presents a significant bottleneck. In our new paper, 2511.04661, led by PhD student Dily Duan Yi Ong with supervisor Will Handley, we introduce unimpeded, a public data repository and Python library designed to democratize advanced cosmological analysis. By providing pre-computed nested sampling chains, unimpeded allows researchers to bypass the most computationally intensive steps of model comparison and tension quantification, accelerating the pace of discovery.

A Community Resource for Bayesian Cosmology

While Markov Chain Monte Carlo (MCMC) methods are excellent for parameter estimation, they cannot compute the Bayesian evidence required for robustly comparing different cosmological models or quantifying tensions between datasets. Nested sampling, as pioneered by Skilling (10.1214/06-BA127), is specifically designed for this purpose. The unimpeded repository serves as an analogue to the Planck Legacy Archive but for nested sampling, offering a “ground truth” grid of results generated with the powerful PolyChord sampler (1506.00171). This resource enables the entire community to perform sophisticated Bayesian analyses without needing access to high-performance computing clusters for chain generation.

The initial release encompasses a comprehensive grid, analyzing:

• Eight Cosmological Models: The standard six-parameter $\Lambda$CDM model plus seven well-motivated extensions, including models with spatial curvature ($\Omega_k$), varying dark energy equations of state ($w$ and $w_0w_a$), massive neutrinos, and primordial gravitational waves.
• Thirty-Nine Datasets: A wide range of observational probes, including the Cosmic Microwave Background (Planck and CamSpec), Baryon Acoustic Oscillations (SDSS), Type Ia Supernovae (Pantheon and SH0ES), and weak lensing (DES Y1), analyzed both individually and in pairwise combinations.

Model Comparison: ΛCDM Remains Robust

Our systematic model comparison reveals a compelling trend. While individual datasets often show mild preferences for various extensions to the standard model, these preferences tend to wash out when multiple, independent datasets are combined. In joint analyses, the base $\Lambda$CDM model is consistently preferred. This suggests that the evidence for new physics seen in isolated probes may be driven by statistical fluctuations or subtle systematic effects, which are diluted by the statistical power of combined data. The unimpeded grid underscores the remarkable robustness and predictive power of the standard cosmological model against the current compendium of observational data.

Characterizing Cosmological Tensions

A key application of the unimpeded grid is the systematic quantification of tensions between cosmological datasets. Using a suite of five complementary statistics, building on methodologies outlined in works such as 2103.12345, we move beyond a simple significance value to characterize the nature of these disagreements. Our key findings include:

• Significant Tensions Confirmed: We identify the most significant tensions within $\Lambda$CDM to be between the Dark Energy Survey (DES) and Planck data ($\sigma=3.57$) and between the SH0ES local distance ladder measurement and Planck ($\sigma=3.27$).
• The $S_8$ Tension is High-Dimensional: The conflict between DES and Planck, often termed the “$S_8$ tension,” manifests as a high-dimensional disagreement ($d_G=6.62$). This indicates a broad inconsistency across multiple parameter directions. Notably, this tension is significantly alleviated in models with additional degrees of freedom, such as a time-varying dark energy equation of state.
• The Hubble Tension is Low-Dimensional and Persistent: In stark contrast, the Hubble tension (SH0ES vs. Planck) is a sharp, low-dimensional conflict ($d_G=1.36$). It is concentrated primarily in the value of $H_0$ and stubbornly persists across nearly all of the seven model extensions we tested.

This nuanced, multi-metric approach reveals that not all tensions are alike. The resolvability of the $S_8$ tension in extended models offers a potential path toward new physics, whereas the persistence of the Hubble tension suggests a more fundamental challenge to our understanding. The unimpeded resource provides the essential tools for the community to continue investigating these cosmic puzzles with statistical rigor and reproducibility.

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