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 \equiv ( \mu _ { obs } - \mu _ { lab } ) / \mu _ { lab } and \Delta \alpha / \alpha \equiv ( \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 \pm 4 _ { stat } \pm 3 _ { sys } ) \times 10 ^ { -9 } , and | \Delta \alpha / \alpha| < 1.1 \times 10 ^ { -7 } .
If only a conservative upper limit is considered , then | \Delta \mu / \mu| \leq 3 \times 10 ^ { -8 } .
We also reviewed and re-analyzed the available data on the cosmological variation of \alpha obtained from Fe i and Fe ii 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| < 2 \times 10 ^ { -6 } was found from the Fe ii system at z = 1.15 towards the bright quasar HE 0515–4414 .
The limit of 2 \times 10 ^ { -6 } corresponds to the utmost accuracy which can be reached with available to date optical facilities .