Uniting the Observed Dynamical Dark Energy Preference with the Discrepancies in Ω_m and H₀ across Cosmological Probes

Recent results from Type Ia supernovae, baryon acoustic oscillations (BAOs), and the cosmic microwave background (CMB) indicate (1) potentially discrepant measurements of the matter density Ω_m and Hubble constant H₀ in the ΛCDM model when analyzed individually and (2) hint of dynamical dark energy in a w₀w_aCDM model when data are combined in a joint analysis. We examine whether underlying dynamical dark energy cosmologies favored by data would result in biases in Ω_m and H₀ for each probe when analyzed individually under ΛCDM. We generate mock data sets in w₀w_aCDM cosmologies, fit the individual probes under the ΛCDM model, and find that expected biases in Ω_m are ∼0.03. Notably, the Ω_m differences between probes are consistent with values observed in real data sets. We also observe that mock DESI-BAO data sets generated in the w₀w_a CDM cosmologies will lead to a biased measurement of H₀ higher by ∼1.2 km s⁻¹ Mpc⁻¹ when fitted under ΛCDM, appearing to mildly improve the Hubble tension, but as the true underlying H₀ is lower, the tension is in fact worsened. We find that the Ω_m discrepancies, the high BAO H₀ relative to the CMB, and the joint dynamical dark energy signal are all related effects that could be explained simultaneously with either new physics or new systematics. While it is possible to unite many of the discrepancies seen in recent analyses along a single axis, our results underscore the importance of understanding systematic differences in data sets, as they have unique impacts in different cosmological parameter spaces.