Limits on the spatial variations of the electron-to-proton mass ratio in the Galactic plane

Aims. We aim to validate the Einstein equivalence principle (local position invariance) by limiting the fractional changes in the electron-to-proton mass ratio, mu = m(e)/m(p), measured in Galactic plane objects. Methods. High-resolution spectral observations of dark clouds in the inversion line of NH3(1, 1) and pure rotational lines of other molecules (the so-called ammonia method) were performed at the Medicina 32-m and the Effelsberg 100-m radio telescopes to measure the radial velocity offsets, Delta RV = V-rot-V-inv, between the rotational and inversion transitions, which have different sensitivities to the value of mu. Results. In our previous observations (2008-2010), a mean offset of = 0.027 +/- 0.010 km s(-1) (3 sigma confidence level (C.L.)) was measured. To test for possible hidden errors, we carried out additional observations of a sample of molecular cores in 2010-2013. As a result, a systematic error with an amplitude similar to 0.02 km s(-1) in the radial velocities was revealed. The averaged offset between the radial velocities of the rotational transitions of HC3N(2-1), HC5N(9-8), HC7N(16-15), HC7N(21-20), and HC7N(23-22), and the inversion transition of NH3(1, 1) is = 0.003 +/- 0.018 km s(-1) (3 sigma C. L.). This value, when interpreted in terms of Delta mu/mu = (mu(obs) - mu(lab))/mu(lab), constraints the mu-variation at the level of Delta mu/mu < 2 x 10(-8) (3 sigma C. L.), which is the most stringent limit on the fractional changes in mu based on astronomical observations.