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Consistency of standard cosmologies using Bayesian model comparison and tension quantification

Lukas Tobias Hergt*, Sophie Henrot-Versillé, and Matthieu Tristram

Douglas Scott

  • *Contact author: lukas.hergt@ijclab.in2p3.fr
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Phys. Rev. D 114, 083531 – Published 19 October, 2026

DOI: https://doi.org/10.1103/7q45-nhmf

Abstract

We present a unified Bayesian assessment of model comparison and dataset consistency for ΛCDM (cold dark matter plus a cosmological constant) and minimal extensions (neutrino mass, spatial curvature, and constant or evolving dark energy) using cosmic microwave background (CMB), baryon acoustic oscillation (BAO), and type Ia supernova (SN) data. The major results are summarized in the first three figures. We quantify model preference with Bayesian evidence and assess consistency with complementary evidence- and likelihood-based diagnostics applied uniformly across dataset combinations. For the models considered, updated planck processing systematically improves internal CMB consistency (low-ℓ versus high-ℓ, and primary CMB versus CMB lensing). The preference for a closed geometry and an associated “curvature tension” with BAO and/or CMB lensing are largely confined to earlier planck likelihood implementations and weaken substantially when using updated CMB processing and more recent BAO measurements. Apparent evidence for evolving dark energy in CMB+BAO+SN combinations depends sensitively on the specific pairing of CMB and SN likelihoods: plausible alternatives shift inferred tensions by more than 1σ and can completely reverse the preferred model. Allowing a free neutrino mass tends to absorb residual shifts without introducing new inconsistencies, and we do not find robust evidence for a standalone τ-driven discrepancy once the full likelihood context is accounted for. We conclude that claims of a required update of our standard cosmological model from ΛCDM to w0waCDM are premature.

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Phys. Rev. D 114, 083531– Published 19 October, 2026
  • Received 30 March 2026
  • Accepted 3 September 2026
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