Exploring the Evidence for Evolving Dark Energy with the Jeffreys prior

Abstract

We investigate the impact of applying the uninformative Jeffreys prior in a re-analysis of DESI DR2 BAO, Planck 2018 CMB, and Type Ia Supernovae (DES-SN5YR, DES-Dovekie, Pantheon+, Union3). We incorporate this prior into new posterior inference and evidence calculations. We introduce novel techniques for interpreting the Jeffreys prior physically. To overcome the computational expense of the Jeffreys prior, we develop a fully $\texttt{JAX}$-based pipeline consisting of $\texttt{CosmoPower-JAX}$ emulators, gradient-based posterior inference using the No-U-Turn Sampler (NUTS), and evidence calculations using $\texttt{JAX}$-accelerated nested sampling. We demonstrate that while the parameter constraints on $w_0$ and $w_a$ remain robust to prior choice (exhibiting only minor shifts of the marginalised posterior towards the $\textit{Maximum A Posteriori}$ in less constraining dataset combinations), the Bayesian evidence is highly sensitive to the use of the Jeffreys prior; replacing uniform priors with the Jeffreys prior reverses the model-selection preference in dataset combinations that favour dynamical dark energy under the uniform prior, while strengthening existing preferences for $Λ$CDM. This is driven primarily by the significantly larger Occam penalty applied by the Jeffreys prior which penalises the overfitting of the data by a $w_0w_a$CDM model.