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

Abstract

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 $|\Delta \alpha /\alpha |=2.10_{-39.26}^{+32.56}\times 10^{-7}$ and $|\Delta \mu /\mu |=1.61_{-34.67}^{+37.16}\times 10^{-7}$ for modified gravity parameter $\gamma \simeq -3.69\times 10^{13}{\mathrm{cm}}^2$, while for the finite temperature case, these are $|\Delta \alpha /\alpha |=1.60_{-35.42}^{+37.31}\times 10^{-7}$ and $|\Delta \mu /\mu |=1.23_{-35.71}^{+37.02}\times 10^{-7}$ 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.

7 pages with 5 figures; accepted for publication in MNRAS

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