  Only astronomical observations can effectively probe in space-time the
variabil ity of the physical dimensionless constants such as the fine structure
constant and proton-to-electron mass ratio, \mu, which are related to fund
amental forces of nature. Several theories beyond the Standard Model (SM) allow
fundamental constants to vary, but they cannot make quantitative predictions so
that only laboratory experiments and astronomical observations can show if th
is is the case or set the allowed bounds. At the moment of writing there are c
laims for a variability of both \alpha and \mu at 5 and 4\sigma of C.L.,
respectively, although for \alpha they are contrasted by null results. The
observations are challenging and a new spectrograph such as ESPRESSO at the
combined incoherent focus of 4 VLT units (a potential 16 m equivalent
telescope) will allow for a significant improvement in the precision
measurement clearing up the controversy. If the variations will be confirmed,
the implications are far reaching, revealing new physics beyond the SM and
pointing a direction for GUTs theories. A most exciting ossibility is that a
variation of \alpha is induced by quintessence through its coupling with the
electromagnetic field. If this is the case an accurate measurement of the
variability could provide a way for reconstructing the equation of state of
Dark Energy (Avelino et al 2006).
