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.