Key drivers of the preference for dynamic dark energy

Joint analysis of the baryon acoustic oscillations (BAO) measurement by the Dark Energy Spectroscopic Instrument (DESI) first data release, Type Ia supernovae (SNe) of the Dark Energy Survey Year 5 (DES5YR) release and cosmic microwave background (CMB) data favors a quintom-like dynamic dark energy model over the standard Lambda cold dark matter ($\Lambda$CDM) model at $3.9\sigma$ level (Adame et al. 2024). We confirm the previous finding in the literature that the preference for dynamic dark energy does not rely on the detailed modeling of CMB physics and remains at a similar significance level ($3.2\sigma$) when the full CMB likelihood is replaced by a CMB acoustic-oscillation angle ($\theta_\star$) prior and a baryon abundance ($\Omega_bh^2$) prior. The computationally efficient $\theta_\star$ and $\Omega_bh^2$ priors allow us to take a frequentist approach by comparing DES5YR SNe and DESI BAO with a large number ($\gtrsim 10^4$) of Planck-constrained $\Lambda$CDM simulations. We find that $\geq 3.2\sigma$ preference for dynamic dark energy is very rare (occurrence rate = $0.28\%$) in simulations. When we combine DESI BAO with SN simulations or combine DES5YR SNe with BAO simulations, the occurrence rate of $\geq 3.2\sigma$ preference for dynamic dark energy increases to $1.2\%$ and $4.8\%$, respectively. These results indicate an internal inconsistency, i.e., a significant tension between DESI BAO + DES5YR SNe and Planck-constrained $\Lambda$CDM models in both Bayesian and frequentist points of view. Although both DESI BAO and DES5YR SNe contribute to the preference for dynamic dark energy, the contribution from DES5YR SNe is more significant. In the frequentist point of view, even DES5YR SNe alone is in tension with Planck-constrained $\Lambda$CDM models, though in Bayesian point of view this tension is prior dependent and inconclusive.