Cosmography via Gaussian process with gamma ray bursts

Abstract

In this paper, we firstly calibrate the Amati relation (the E p - E 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 order and the redshift z ∼ 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 ∼ 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 ΛCDM 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.