  Spatial and temporal variations in the electron-to-proton mass ratio, mu, and
in the fine-structure constant, alpha, are predicted in non-Standard models
aimed to explain the nature of dark energy. Among them the so-called
chameleon-like scalar field models predict strong dependence of masses and
coupling constants on the local matter density. To explore such models we
estimated the parameters Delta mu/mu = (mu_obs - mu_lab)/mu_lab and Delta
alpha/alpha = (alpha_obs - alpha_lab)/alpha_lab in two essentially different
environments, - terrestrial (high density) and interstellar (low density), -
from radio astronomical observations of cold prestellar molecular cores in the
disk of the Milky Way. We found that Delta mu/mu = (22 +/- 4_stat +/-
3_sys)x10^{-9}, and |Delta alpha/alpha| < 1.1x10^{-7}. If only a conservative
upper limit is considered, then |Delta mu/mu| <= 3x10^{-8}. We also reviewed
and re-analyzed the available data on the cosmological variation of alpha
obtained from FeI and FeII systems in optical spectra of quasars. We show that
statistically significant evidence for the changing alpha at the level of
10^{-6} has not been provided so far. The most stringent constraint on |Delta
alpha/alpha| < 2x10^{-6} was found from the FeII system at z = 1.15 towards the
bright quasar HE0515-4414. The limit of 2x10^{-6} corresponds to the utmost
accuracy which can be reached with available to date optical facilities.
