Limits on the spatial variations of the electron-to-proton mass ratio in
  the Galactic plane
  Aims. 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 <Delta RV> = 0.027+/-0.010 km/s [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 in the radial velocities of an
amplitude ~0.02 km/s 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) <Delta
RV> = 0.003+/-0.018 km/s (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*10^{-8} (3 sigma C.L.), which is the most stringent
limit on the fractional changes in mu based on astronomical observations.
