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The ammonia method to probe variations of the electron-to-proton mass ratio,Delta_mu/mu, is applied for the first time to dense prestellar molecular cloudsin the Milky Way. Carefully selected sample of 21 NH_3/CCS pairs observed inthe Perseus molecular cloud provide the offset Delta V (CCS-NH_3)=36+/-7_{stat}+/-13.5_{sys} m/s . A similar offset of Delta V = 40.8 +/-12.9_{stat} m/s between NH_3 (J,K) = (1,1) and N_2H+ J = 1-0 has been found inan isolated dense core L183 by Pagani et al. (2009). Overall these observationsprovide a safe bound of a maximum offset between ammonia and the othermolecules at the level of Delta V < 100 m/s. This bound corresponds toDelta_mu/mu < 1E-7, which is an order of magnitude more sensitive thanavailable extragalactic constraints. Taken at face value the measured Delta Vshows positive shifts between the line centers of NH_3 and these two othermolecules and suggest a real offset, which would imply a Delta_mu/mu about4E-8. If Delta_mu/mu follows the gradient of the local gravitational potential,then the obtained results are in conflict with laboratory atomic clockexperiments in the solar system by 5 orders of magnitude, thus requiring achameleon-type scalar field model. New measurements involving other moleculesand a wider range of objects along with verification of molecular restfrequencies are currently planned to confirm these first indications.

Stringent bounds to spatial variations of the electron-to-proton mass ratio in the Milky Way