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

TL;DR

The paper investigates whether the apparent preference for dynamical dark energy from DES-5Y plus DESI BAO can be explained by a low-redshift supernova magnitude offset rather than true dark energy evolution. It extends flexknot reconstructions with a low-$z$ offset parameter $\Delta m_{\mathrm B}$, and compares Bayesian evidences among $\Lambda$CDM, CPL, and flexknots using nested bridge sampling and a GPU-accelerated $JAX$ implementation. The main finding is that, when DESI BAO is included, the evidence strongly favors offset $\Lambda$CDM over dynamical models, suggesting the signal may be driven by SN systematics; without DESI the offset evidence is weaker. The work highlights the importance of accounting for SN systematics in cosmological inferences and demonstrates fast, robust Bayesian model selection methods (NBS and JAX) for cosmology.

Abstract

DES-5Y supernovae, combined with DESI BAO, appear to favour Chevallier-Polarski-Linder $(w_0, w_a)$ dynamical dark energy over $Λ$CDM. arXiv:2408.07175 suggested that this is driven by a systematic in the DES pipeline, which particularly affects the low-redshift supernovae brought in from legacy surveys. It is difficult to investigate these data in isolation, however, as the complicated supernovae pipelines must properly account for selection effects. In this work, we discover that the Bayesian evidence previously found for flexknot dark energy (arXiv:2503.17342) is beaten by a magnitude offset between the low- and high-redshift supernovae. In addition, we find that the possible tension between DES-5Y and DESI is significantly reduced by such an offset. We also take the opportunity to trial Nested Bridge Sampling with Sequential Monte Carlo as an alternative method for calculating Bayes factors.

Figures (5)

• Figure 1: Prior and posterior of CPL and $n=2$ flexknot, using DES-5Y combined with DESI BAO. The top panel shows the $(w_0, w_a)$ projection, the lower panel shows $(w_0, w_{n-1})$. Prior samples are shown as a scatter, the posteriors are shown as kernel density estimates. For reference, the cross marks $\Lambda$CDM. The two posteriors are so similar that it is challenging to see one on top of the other!
• Figure 2: Flexknot reconstruction of the dark energy equation of state parameter using DES-5Y supernovae only. In red is the standard likelihood, in lilac, the version with the $\Delta m_\mathrm B$ offset for the low-redshift supernovae. The overall shape of the reconstructions are very similar, but the functional KL divergence and model evidences tell quite different stories. Firstly, note that the high-$a$/low-redshift KL divergence lacks the peak just below $z=0.1$, which is to be expected as allowing those magnitudes to float up and down will naturally reduce their constraining power. Second, note that the evidence for $\Lambda$CDM has increased with the offset, meanwhile, it has fallen for all flexknots with more than three knots. The Bayes factor between $\Lambda$CDM and $w$CDM is similar between the two likelihoods, but $n=2$ is more disfavoured with the offset likelihood. Crucially, the evidence for $\Lambda$CDM with the offset is greater than the flexknots without the offset. This suggests that the complexity demanded by the flexknot model is just as well, if not better, met by including this additional degree of freedom. Please note that the posteriors shown in the bottom-left panels do not include $\Lambda$CDM, which is shown separately in Figure \ref{['fig:dmb']}. With flexknots, $\Delta m_\mathrm B$ is not well constrained.
• Figure 3: Similar to Figure \ref{['fig:des5y']}, this time with the addition of DESI BAO. This time, it is even clearer that $\Lambda$CDM with the $\Delta m_\mathrm B$ offset is the favoured model. Once again, the low-redshift KL divergence peak is lost with the additional parameter. Unlike the results with DES-5Y alone, the Bayes factor for $\Lambda$CDM with $\Delta m_\mathrm B$ over almost any other model is "decisive". Again, please note that the posteriors shown in the bottom-left panels do not include $\Lambda$CDM, these are shown in Figure \ref{['fig:dmb']}.
• Figure 4: Tension values between DES-5Y and DESI BAO, with and without the low-redshift offset. $\Lambda$CDM is shown as horizontal dashed lines, for easy comparison with the other points. For $\Lambda$CDM the tension has been reduced (more positive) significantly, while for $w$CDM and CPL, it has increased slightly. $\Lambda$CDM with the offset is now on-par with CPL, though $w$CDM remains the model with the best dataset concordance. In contrast, without the offset, $\Lambda$CDM is the most discrepant model of all. For three knots and above, the tension is similar with or without the offset.
• Figure 5: Posterior histograms of $\Delta m_\mathrm B$ for $\Lambda$CDM and CPL. The left panel uses DES-5Y only, the right also includes DESI BAO. The prior is uniform over the domain of the plot. As predicted by georgedes5y, its value is centred on $-0.04$. Note that the $\Lambda$CDM posteriors (and the right CPL posterior) are well contained within the prior, therefore, the evidence which would have been found had a wider prior been used can be easily be computed with the ratio of the prior volumes.