Refining fundamental constants with white dwarfs: machine learning informed constraints on fine-structure constant and proton-to-electron mass ratio

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. Utilising high-precision white dwarf observations from the Gaia-DR3 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 $\mathrm{\mid }\mathrm{\Delta }\alpha \mathrm{/}\alpha \mathrm{\mid }=2.10_{-39.26}^{+32.56}\times {10}^{-7}$ and $\mathrm{\mid }\mathrm{\Delta }\mu \mathrm{/}\mu \mathrm{\mid }=1.61_{-34.67}^{+37.16}\times {10}^{-7}$ for modified gravity parameter $\gamma \simeq -3.69\times {10}^{13}{\mathrm{c}\mathrm{m}}^2$, while for the finite temperature case, these are $\mathrm{\mid }\mathrm{\Delta }\alpha \mathrm{/}\alpha \mathrm{\mid }=1.60_{-35.42}^{+37.31}\times {10}^{-7}$ and $\mathrm{\mid }\mathrm{\Delta }\mu \mathrm{/}\mu \mathrm{\mid }=1.23_{-35.71}^{+37.02}\times {10}^{-7}$ for $T\simeq 1.1\times {10}^7\mathrm{K}$. 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.