Measuring the spatio-temporal variation of fundamental physical constants using the OH sum rules

In this paper, we introduce a method to constrain the variation of fundamental physical constants predicted by grand unified theories. This approach utilizes OH sum rules, which exhibit different forms depending on the physical conditions of the OH gas. Employing a least-squares technique, we can directly derive the relative velocity offsets among four OH lines in each ground state. This circumvents the need for spectral profile fitting, which is often unfeasible for spectra with complex profiles. Moreover, this method remains robust even when portions of the spectra are contaminated by radio frequency interference (RFI). Applying this method to a Galactic source G035.1+0.5, we obtained a stringent constraint of ΔX/X=(-1.8 plus or minus5.1) times10-6, where X=μ-1α squaredg p 0.54. This method is expected to play a crucial role in extracting fundamental physics from large datasets of upcoming Square Kilometre Array (SKA) telescope.