Dynamic or Systematic? Bayesian model selection between dark energy and supernova biases

In our latest work, 2509.13220, we tackle a critical question at the heart of modern cosmology: is the apparent preference for evolving dark energy in recent supernova data a sign of new physics, or the ghost of a hidden systematic? This research, led by A. N. Ormondroyd with W. J. Handley, M. P. Hobson, A. N. Lasenby, and D. Yallup, employs rigorous Bayesian model selection to adjudicate between these two compelling possibilities.

The Cosmological Conundrum

Recent analyses combining the Dark Energy Survey 5-year (DES-5Y) Type Ia supernovae data with Baryon Acoustic Oscillation (BAO) measurements from DESI have hinted that the Universe may favour a dynamical dark energy model over the standard cosmological constant, $\Lambda$CDM. Work by Efstathiou (2408.07175) suggested this result could be driven by a systematic magnitude offset in the low-redshift supernovae, which DES-5Y incorporates from legacy surveys. Disentangling such effects is notoriously difficult due to the complex data processing pipelines required to standardise supernovae as cosmological probes.

Instead of discarding data or assuming a specific offset, we take a principled Bayesian approach. We introduce a new, free parameter, $\Delta m_\mathrm{B}$, into our model, which represents a potential magnitude offset applied only to the low-redshift, non-DES supernovae. This allows the data itself to tell us whether such a systematic is preferred over a more complex cosmological model.

A Flexible Approach to Model Selection

To perform this test, we extend the “flexknot” reconstruction framework developed in our previous papers (2503.17342). Flexknots provide a model-independent way to reconstruct the dark energy equation of state, $w(a)$, allowing for a wide range of possible evolutionary histories. By comparing the Bayesian evidence for various models, we can quantitatively assess which hypothesis provides the most economical explanation for the data. The models under consideration are:

• Standard $\Lambda$CDM (with and without the $\Delta m_\mathrm{B}$ offset).
• The CPL parameterisation (with and without the offset).
• Our free-form flexknot reconstructions (with and without the offset).

All calculations are performed using our group’s advanced nested sampling algorithm, PolyChord, which is designed for precisely this kind of challenging parameter estimation and model selection problem.

Decisive Evidence for a Systematic Offset

Our results are striking. When DES-5Y data is combined with DESI BAO, the Bayesian evidence decisively favours the simple $\Lambda$CDM model that includes the $\Delta m_\mathrm{B}$ systematic offset. The log-Bayes factor is approximately 4, indicating very strong evidence for the offset model over standard $\Lambda$CDM. Crucially, this simple systematic model is also strongly preferred over all dynamical dark energy alternatives, including CPL and the more flexible flexknot reconstructions. The posterior for the offset parameter, $\Delta m_\mathrm{B}$, is centred around $-0.045 \pm 0.012$, in remarkable agreement with previous suggestions.

Furthermore, introducing this offset parameter significantly reduces the statistical tension between the DES-5Y and DESI datasets for the $\Lambda$CDM model. Without the offset, $\Lambda$CDM is the most discrepant model; with it, its concordance becomes comparable to that of the CPL model. This finding reinforces the conclusion that the systematic offset provides a better explanation for the data concordance issues than invoking new physics.

In summary, this work suggests that the observed preference for dynamical dark energy in the combined DES-5Y and DESI datasets is better explained as a systematic offset between the low- and high-redshift supernova samples. While this does not rule out the possibility of dynamical dark energy—a cornerstone of modern physics since its initial discovery ([10.1086/300499])—it demonstrates that a simpler, data-internal explanation is overwhelmingly preferred by the evidence. This study highlights the power of Bayesian methods to navigate the complex interplay between systematics and fundamental physics, a central theme of our group’s research philosophy.

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