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

## TL;DR

This study uses machine learning and white dwarf observations to place new, tighter constraints on possible variations of fundamental constants, considering effects of gravity and temperature.

## Contribution

It introduces a Bayesian-inspired machine learning approach to relate white dwarf properties with fundamental constants, accounting for gravity and temperature effects.

## Key findings

- Established the strongest constraints on $eta$ and $eta'$ parameters.
- Demonstrated the influence of gravity and temperature on fundamental constant variations.
- Provided tighter bounds than previous studies.

## 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 $|\Delta\alpha/\alpha|=2.10^{+32.56}_{-39.26}\times10^{-7}$ and $|\Delta\mu/\mu|=1.61^{+37.16}_{-34.67}\times10^{-7}$ for modified gravity parameter $\gamma\simeq -3.69\times10^{13}\,\mathrm{cm}^2$, while for the finite temperature case, these are $|\Delta\alpha/\alpha|=1.60^{+37.31}_{-35.42}\times10^{-7}$ and $|\Delta\mu/\mu|=1.23^{+37.02}_{-35.71}\times10^{-7}$ 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.