  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 clouds
in the Milky Way. Carefully selected sample of 21 NH_3/CCS pairs observed in
the 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 in
an isolated dense core L183 by Pagani et al. (2009). Overall these observations
provide a safe bound of a maximum offset between ammonia and the other
molecules at the level of Delta V < 100 m/s. This bound corresponds to
Delta_mu/mu < 1E-7, which is an order of magnitude more sensitive than
available extragalactic constraints. Taken at face value the measured Delta V
shows positive shifts between the line centers of NH_3 and these two other
molecules and suggest a real offset, which would imply a Delta_mu/mu about
4E-8. If Delta_mu/mu follows the gradient of the local gravitational potential,
then the obtained results are in conflict with laboratory atomic clock
experiments in the solar system by 5 orders of magnitude, thus requiring a
chameleon-type scalar field model. New measurements involving other molecules
and a wider range of objects along with verification of molecular rest
frequencies are currently planned to confirm these first indications.

Cosmology and Nongalactic Astrophysics