Gamma-ray Bursts Cosmology with The X-ray Fundamental Plane Relation

Cosmological models with different equations of state from the Λ Cold Dark Matter (ΛCDM) are at the center of the debate between the data of SNe type Ia and the Planck data from the Cosmic Microwave Background. Thus, adding cosmological probes observed at high redshift is desired. Gamma-Ray Bursts (GRBs) are ideal candidates for investigating the expansion of the Universe at high redshift, due to their high luminosities. However, it is challenging using GRB correlations between luminosities and a cosmological independent variable, because GRB luminosities vary widely. We corrected a tight correlation between the rest-frame end time of the plateau, its corresponding X-ray luminosity, and the peak prompt luminosity, the so-called fundamental plane relation, for the jet opening angle. Its dispersion is 0.02 ± 0.04 dex, 94.12% less than the isotropic fundamental plane relation. This is the smallest scatter compared to any current GRB correlation. This shows that GRBs can be used as standard candles. Our results on the Universe matter content and the equation of state using GRBs are in 1 σ with the values obtained with SNe Ia only, but at much larger redshift (up to z=5).