Dynamical Dark Energy Meets Varying Electron Mass: Implications for Phantom Crossing and the Hubble Constant

We investigate the interplay between varying electron mass ($m_e$) and dynamical dark energy by analysing the Chevallier-Polarski-Linder (CPL) parametrization and its non-crossing variants, both with and without a varying-$m_e$ component. Our aim is to assess whether the preference for late-time dynamics and phantom divide line (PDL) crossing persists when early-time physics is introduced, and whether these combined models improve the alleviation of the Hubble tension compared to the varying-$m_e$ extension alone. Using the latest CMB, BAO, and supernova datasets, we derive updated constraints on $\Lambda$CDM, CPL, and their extensions, and examine their impact on $H_0$ and the preference for late-time dynamics. We find that $\Lambda$CDM+$m_e$ yields the largest upward shift in $H_0$, while replacing $\Lambda$ with the CPL parametrization or its non-crossing variants provides modest improvements in the overall fit. The data consistently favour dynamical dark energy and a phantom divide line crossing at scale factors $a_{\rm c}\simeq0.6-0.9$, and these preferences remain robust, though somewhat weaker ($\gtrsim2\sigma$), when the electron mass is also allowed to vary. Among the late-time models, CPL performs better than its non-crossing variants, further reinforcing the evidence for a genuine phantom divide crossing. The alleviation of the $H_0$ tension in the varying-$m_e$ case arises from late-time data breaking the strong $\Omega_m$-$m_e$ degeneracy in the CMB, while the additional degrees of freedom in CPL models allow the late-time dynamics to absorb this impact, thereby weakening the degeneracy breaking and further lowering $H_0$ through their ability to yield a decreasing dark energy contribution.