Reconstruction of the Cosmic Equation of State for High Redshift
  We investigate the possibilities of reconstructing the cosmic equation of
state (EoS) for high redshift. In order to obtain general results, we use two
model-independent approaches. The first reconstructs the EoS using comoving
distance and the second makes use of the Hubble parameter data. To implement
the first method, we use a recent set of Gamma-Ray Bursts (GRBs) measures. To
implement the second method, we generate simulated data using the Sandage-Loeb
($SL$) effect; for the fiducial model, we use the $\Lambda CDM$ model. In both
cases, the statistical analysis is conducted through the Gaussian processes
(non-parametric). In general, we demonstrate that this methodology for
reconstructing the EoS using a non-parametric method plus a model-independent
approach works appropriately due to the feasibility of calculation and the ease
of introducing a priori information ($H_ {0}$ and $\Omega_{m0}$). In the near
future, following this methodology with a higher number of high quality data
will help obtain strong restrictions for the EoS.
