Limits on the space-time variations of fundamental constants

We report on new tests that improve our previous (2009-2010) estimates of the electron-to-proton mass ratio variation, mu = m_e/m_p. Subsequent observations (2011-2013) at the Effelsberg 100-m telescope of a sample of eight molecular cores from the Milky Way disk reveal systematic errors in the measured sky frequencies varying with an amplitude +/-0.01 km/s during the exposure time. The averaged offset between the radial velocities of the NH3(1,1), HC3N(2-1), HC5N(9-8), HC7N(16-15), HC7N(21-20), and HC7N(23-22) transitions gives Delta V = 0.002 +/- 0.015 km/s [3 sigma confidence level (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 < 2x10^{-8} (3 sigma C.L.), which is the most stringent limit on the fractional changes in mu based on radio astronomical observations.