Uniting the Observed Dynamical Dark Energy Preference with the Discrepancies in $Ω_m$ and $H_0$ Across Cosmological Probes

Abstract: Recent results from Type Ia Supernovae (SNe), baryon acoustic oscillations (BAO), and the cosmic microwave background (CMB) indicate 1) potentially discrepant measurements of the matter density $\Omega_m$ and Hubble constant $ H_0 $ in $\Lambda$CDM model when analyzed individually, and 2) hints of dynamical dark energy in a $w_0w_a$CDM 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 $\Omega_m$ and $ H_0 $ for each probe when analyzed individually under $\Lambda$CDM. We generate mock datasets in $w_0w_a$CDM cosmologies, fit the individual probes under the $\Lambda$CDM model, and find expected biases in $\Omega_m$ are $\sim 0.03$. Notably, the $\Omega_m$ differences between probes are consistent with values observed in real datasets. We also observe that mock DESI-BAO datasets generated in the $w_0w_a$CDM cosmologies will lead to a biased measurement of $H_0$ higher by ($\sim1.2$km/s/Mpc) when fitted under $\Lambda$CDM, appearing to mildly improve the Hubble tension, but as the true underlying $H_0$ is lower, the tension is in fact worsened. We find that the $\Omega_m$ discrepancies, the high BAO $ H_0 $ relative to CMB, and the joint dynamical dark energy signal are all related effects that could be explained \textit{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 datasets, as they have unique impacts in different cosmological parameter spaces.