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

TL;DR

This work investigates whether combining an early-time modification (varying electron mass) with late-time dynamical dark energy (CPL and non-crossing variants) can address the H0 tension and the phantom divide crossing. Using a CLASS/Cobaya framework with PPF, HyRec, and a comprehensive dataset (Planck, ACT, SPT, DESI/SDSS BAO, Pantheon+), the authors quantify how these components interact. They find that varying $m_e$ alone yields the largest upward shift in $H_0$, while CPL-type late-time dynamics provide only modest fit improvements and do not surpass the $H_0$ gains from $m_e$; PDL crossing remains favored across analyses, even with varying $m_e$. The results suggest that simple late-time extensions can undermine the $H_0$ relief offered by early-time $m_e$ changes, indicating a need for more physically consistent or coupled models to responsibly combine early- and late-time modifications.

Abstract

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 $Λ$CDM, CPL, and their extensions, and examine their impact on $H_0$ and the preference for late-time dynamics. We find that $Λ$CDM+$m_e$ yields the largest upward shift in $H_0$, while replacing $Λ$ 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 ($\gtrsim2σ$), 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 $Ω_m$-$m_e$ 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.

Figures (7)

• Figure 1: Evolution of the dark energy equation of state $w(a)$ for the CPL model and its non-crossing variants, shown with and without a varying electron mass. Solid lines correspond to the baseline models, while dashed lines indicate their varying-$m_e$ counterparts. Parameter values are taken from the best fits in \ref{['tab:all_act_constraints']}, using the CMB-A+DESI+PP dataset.
• Figure 2: Triangle plot comparing parameter constraints for the four models with a varying electron mass: $\Lambda$CDM+$m_e$, CPL+$m_e$, $\textnormal{CPL}_{<a_{\rm c}}$+$m_e$, and $\textnormal{CPL}_{>a_{\rm c}}$+$m_e$. Results are based on the CMB-A+DESI+PP dataset combination, showing that all models share the same correlation directions among $m_e$, $H_0$, $\Omega_m$, and $\sigma_8$ but differ in the tightness of their constraints.
• Figure 3: Comparison of the posterior distributions of the CPL dark energy model with and without a varying electron mass, using CMB-A+PP combined with either DESI BAO (left) or SDSS BAO (right). Two-dimensional contours in the $w_0$–$w_a$ plane for CPL+$m_e$ (blue and dotted blue) and standard CPL (orange), with dashed lines showing example lines of constant crossing scale $a_{\rm c}$. Dotted lines illustrate $w_a = 0$ vertically and $w_0 = -1$ horizontally, with the intersection corresponding to $w(a) = -1$ at all redshifts.
• Figure 4: One-dimensional posterior distributions of the phantom-divide crossing scale factor, $a_{\rm c}$, for the CPL model, shown for different dataset combinations. Solid lines correspond to CMB-A+DESI+PP, dashed lines to CMB-A+SDSS+PP, and dotted lines to CMB-A+DESI. Orange curves represent the base CPL extension, while blue curves show CPL models including a varying electron mass.
• Figure 5: Triangle plot based on the CMB-A+DESI+PP data combination showing 2D contours and 1D posteriors for $\{w_0, w_a, m_e/m_{e,0}\}$, highlighting correlations in the space of extra free parameters.