Assessing the viability of successful reconstruction of the dynamics of
  dark energy using varying fundamental couplings
  We assess the viability of successful reconstruction of the evolution of the
dark energy equation of state using varying fundamental couplings, such as the
fine structure constant or the proton-to-electron mass ratio. We show that the
same evolution of the dark energy equation of state parameter with cosmic time
may be associated with arbitrary variations of the fundamental couplings.
Various examples of models with the same (different) background evolution and
different (the same) time variation of fundamental couplings are studied in the
letter. Although we demonstrate that, for a broad family of models, it is
possible to redefine the scalar field in such a way that its dynamics is that
of a standard quintessence scalar field, in general such redefinition leads to
the breakdown of the linear relation between the scalar field and the variation
of fundamental couplings. This implies that the assumption of a linear coupling
is not sufficient to guarantee a successful reconstruction of the dark energy
dynamics and consequently additional model dependent assumptions about the
scalar field responsible for the dark energy need to be made.
