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The correlation between the peak spectra energy ($E_p$) and the equivalentisotropic energy ($E_{\rm iso}$) of long gamma-ray bursts (GRBs), the so-calledAmati relation, is often used to constrain the high-redshift Hubble diagram.Assuming Lambda cold dark matter ($\Lambda$CDM) cosmology, Wang et al. found a$\gtrsim 3\sigma$ tension in the data-calibrated Amati coefficients betweenlow- and high-redshift GRB samples. To reduce the impact of fiducial cosmology,we use the Parameterization based on cosmic Age (PAge), an almostmodel-independent framework to trace the cosmological expansion history. Wefind that the low- and high-redshift tension in Amati coefficients stays almostthe same for the broad class of models covered by PAge, indicating that thecosmological assumption is not the dominant driver of the redshift evolution ofGRB luminosity correlation. Next, we analyze the selection effect due to fluxlimits in observations. We find Amati relation evolves much more significantlyacross energy scales of $E_{\rm iso}$. We debias the GRB data by selectivelydiscarding samples to match low-$z$ and high-$z$ $E_{\rm iso}$ distributions.After debiasing, the Amati coefficients agree well between low-$z$ and high-$z$data groups, whereas the evidence of $E_{\rm iso}$-dependence of Amati relationremains to be strong. Thus, the redshift evolution of GRB luminositycorrelation can be fully interpreted as a selection bias, and does not implycosmological evolution of GRBs.

Reconciling low and high redshift GRB luminosity correlations