Cosmography via Gaussian process with gamma ray bursts
Yuhao Mu, Baorong Chang, Lixin Xu
Abstract
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.