Impact of the matter density uncertainty on the dark energy
  reconstruction
  In this paper we study the impact of the fractional matter density
uncertainty in the reconstruction of the equation of state of dark energy. We
consider both standard reconstruction methods, based on the dynamical effect
that dark energy has on the expansion of the Universe, as well as non-standard
methods, in which the evolution of the dark energy equation of state with
redshift is inferred through the variation of fundamental couplings such as the
fine structure constant, $\alpha$, or the proton-to-electron mass ratio, $\mu$.
We show that the negative impact of the matter density uncertainty in the dark
energy reconstruction using varying couplings may be very small compared to
standard reconstruction methods. We also briefly discuss other fundamental
questions which need to be answered before varying couplings can be
successfully used to probe the nature of the dark energy.
