Searching for cosmic-time variation in the gravitational constant with strongest \(\text {H}_2\) Werner transitions

Probing changes in fundamental physics constants over cosmological space-time is a significant area in both theoretical and experimental physics. An effective method for probing these variations is to compare laboratory measurements with astrophysical data. In this study, we utilize a combination of laboratory data and observed Werner transitions of \(\text {H}_2\) in the white dwarf star GD29-38. Our analysis reveals that the temporal variation of the gravitational constant is \(\dot{G}/G = (0.014 \pm 0.096) \times 10^{-15} \, \text {year}^{-1}\), with a gravitational potential of \(\phi \approx 1.9 \times 10^4\) and an average total redshift of \(\text {H}_2\) of \(z_{\text {abs}} = 0.0001360(8)\). This newly established constraint on the time variation of \(G\) plays a crucial role in enhancing discussions within unified theories.