Cosmography via Gaussian Process with Gamma Ray Bursts

In this paper, we firstly calibrate the Amati relation (the $E_{\rm p}-E_{\rm iso}$ correlation) of gamma ray bursts (GRBs) at low redshifts ($z<0.8$) via Gaussian process by using the type Ia supernovae samples from Pantheon+ under the philosophy that objects at the same redshift should have the same luminosity distance in any cosmology. As a result, this calibration derives the distance moduli of GRBs at high redshifts ($z>0.8$). For an application of these derived distance modulus of GRBs to cosmology, via Gaussian process again, a series of cosmography parameters, which describe kinematics of our Universe, up to the fifth oder and the redshift $z\sim 5$, i.e. the Hubble parameter $H(z)$, the deceleration parameter $q(z)$, the jerk parameter $j(z)$, the snap parameter $s(z)$ and the lerk parameter $l(z)$, are reconstructed from the cosmic observations. The reconstructed cosmography parameters show a transition singularity at $z\sim 6$, it may resort to two possible explanations: one is that the GRBs data points at high redshift $z>5$ are still reliable, it means that new physics beyond the $\Lambda$CDM model happens; another one is that the quality and quantity of GRBs data points at high redshift $z>5$ are not good enough to give any viable prediction of the kinematics of our Universe. To pin down this problem, more high redshifts $z>5$ cosmic observational are still needed.