Redshift evolution of the Amati relation: Calibrated results from the Hubble diagram of quasars at high redshifts

Gamma-ray bursts (GRBs) have long been proposed as a complementary probe to type Ia supernovae (SNe Ia) and cosmic microwave background explore the expansion history of high-redshift universe, mainly because they are bright enough be detected at greater distances. Although lack definite physical explanations, many empirical correlations between GRB isotropic energy/luminosity some directly detectable spectral/temporal properties make GRBs standard candles. Since observed rate falls off rapidly low redshifts, thus preventing cosmology independent calibration these correlations. In order avoid circularity problem, SN data usually used calibrate luminosity relations in redshift region (limited by range for sample), then extrapolate it high region. This approach is based on assumption no evolution relations. this work, we suggest use complete quasar sample $0.5<z<5.5$ test such an assumption. We divide into several sub-samples with different bins, each sub-sample $\gamma$-ray equivalent energy relevant bins. By fitting newly calibrated data, find strong evidence that most commonly Amati relation spectral peak isotropic-equivalent radiated shows no, or marginal, redshift. Indeed, coefficients could maximum variation 0.93\% there coincidence 1$\sigma$.