Kinematic constraints beyond $z\simeq0$ using calibrated GRB correlations

The dynamics of the Universe are revised using high-redshift data from gamma-ray bursts to constrain cosmographic parameters by means of model-independent techniques. Considering samples from four gamma-ray burst correlations and two hierarchies up to $j_0$ and $s_0$, respectively, we derived limits over the expansion history of the Universe. Since cosmic data span outside $z\simeq0$, we investigated additional cosmographic methods such as auxiliary variables and Pad\'e approximations. Bezi\'er polynomials were employed to calibrate our correlations and heal the circularity problem. Several Markov chain Monte Carlo simulations were performed on the model-independently calibrated Amati, Ghirlanda, Yonetoku, and combo correlations to obtain $1$--$\sigma$ and $2$--$\sigma$ confidence levels and to test the standard cosmological model. Reasonable results are found up to $j_0$ and $s_0$ hierarchies, respectively, only partially alleviating the tension on local $H_0$ measurements as $j_0$ hierarchy is considered. Discussions on systematic errors have been extensively reported here. Our findings show that the $\Lambda$CDM model is not fully confirmed using gamma-ray bursts. Indications against a genuine cosmological constant are summarized and commented on in detail.