Intrinsic scatter of the luminosity relation, redshift distribution of
  the standard candles, and the constraining capability
  Standard candles are one of the most important tools to study the universe.
In this paper, the constraints of standards candles on the cosmological
parameters are estimated for different cases. The dependence of the constraints
on the intrinsic scatter of the luminosity relation and the redshift
distribution of the standard candles is specifically investigated. The results,
especially for the constraints on the components of the universe, clearly show
that constraints from standard candles at different redshifts have different
degeneracy orientations, thus standard candles with a wide redshift
distribution can self break the degeneracy and improve the constraints
significantly. As a result of this, even with the current level of tightness of
known luminosity relations, gamma-ray bursts (GRBs) can give comparable
tightness of constraint with type Ia supernovae (SNe Ia) on the components of
the universe as long as the redshifts of the GRBs are diversifying enough.
However, for a substantial constraint on the dark energy EOS, tighter
luminosity relations for GRBs are needed, since the constraints on the dark
energy from standard candles at high redshifts are very weak and are thus less
helpful in the degeneracy breaking.
