2025MNRAS.542.3395U

We explore the potential variation of two fundamental constants, the fine-structure constant $\alpha$ and the proton-to-electron mass ratio $\mu$, within the framework of modified gravity theories and finite-temperature effects. Utilizing high-precision white dwarf observations from the Gaia Data Release 3 survey, we construct a robust mass-radius relation using a Bayesian-inspired machine learning framework. This empirical relation is rigorously compared with theoretical predictions derived from scalar-tensor gravity models and temperature-dependent equations of state. Our results demonstrate that both underlying gravitational theory and temperature substantially influence the inferred constraints on $\alpha$ and $\mu$. We obtain the strongest constraints as $|\Delta \alpha /\alpha |=2.10^{+32.56}_{-39.26}\times 10^{-7}$ and $|\Delta \mu /\mu |=1.61^{+37.16}_{-34.67}\times 10^{-7}$ for modified gravity parameter $\gamma \simeq -3.69\times 10^{13}\, \mathrm{cm}^2$, while for the finite temperature case, these are $|\Delta \alpha /\alpha |=1.60^{+37.31}_{-35.42}\times 10^{-7}$ and $|\Delta \mu /\mu |=1.23^{+37.02}_{-35.71}\times 10^{-7}$ for $T \simeq 1.1 \times 10^7\rm \, K$. These findings yield tighter constraints than those reported in earlier studies and underscore the critical roles of gravitational and thermal physics in testing the constancy of fundamental parameters.