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 α and the proton-to-electron mass ratio μ, 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 α and μ. We obtain the strongest constraints as |Δ α /α |=2.10+32.56-39.26× 10⁻⁷ and |Δ μ /μ |=1.61+37.16-34.67× 10⁻⁷ for modified gravity parameter γ -3.69× 10¹³\, cm², while for the finite temperature case, these are |Δ α /α |=1.60+37.31-35.42× 10⁻⁷ and |Δ μ /μ |=1.23+37.02-35.71× 10⁻⁷ for T 1.1 × 10⁷ \, 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.