Variation in the fine-structure constant, distance-duality relation and
  the next generation of high-resolution spectrograph
  The possibility of variation of the fundamental constants of nature has been
a long-standing question, with important consequences for fundamental physics
and cosmology. In particular, it has been shown that variations in the
fine-structure constant, $\alpha$, are directly related to violation of the
distance duality relation (DDR), which holds true as long as photons travel on
unique null geodesics and their number is conserved. In this paper we use the
currently available measurements of ${\Delta \alpha}/{\alpha}$ to impose the
most stringent constraints on departures of the DDR to date, here quantified by
the parameter $\eta$. We also perform a forecast analysis to discuss the
ability of the new generation of high-resolution spectrograph, like
ESPRESSO/VLT and E-ELT-HIRES, to constrain the DDR parameter $\eta$. From the
current data we obtain constraints on $\eta$ of the order of $10^{-7}$ whereas
the forecasted constraints are two orders of magnitude lower. Considering the
expected level of uncertainties of the upcoming measurements, we also estimate
the necessary number of data points to confirm the hypotheses behind the DDR.
