Reconciling low and high redshift GRB luminosity correlations
  The correlation between the peak spectra energy ($E_p$) and the equivalent
isotropic energy ($E_{\rm iso}$) of long gamma-ray bursts (GRBs), the so-called
Amati 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 between
low- and high-redshift GRB samples. To reduce the impact of fiducial cosmology,
we use the Parameterization based on cosmic Age (PAge), an almost
model-independent framework to trace the cosmological expansion history. We
find that the low- and high-redshift tension in Amati coefficients stays almost
the same for the broad class of models covered by PAge, indicating that the
cosmological assumption is not the dominant driver of the redshift evolution of
GRB luminosity correlation. Next, we analyze the selection effect due to flux
limits in observations. We find Amati relation evolves much more significantly
across energy scales of $E_{\rm iso}$. We debias the GRB data by selectively
discarding 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 relation
remains to be strong. Thus, the redshift evolution of GRB luminosity
correlation can be fully interpreted as a selection bias, and does not imply
cosmological evolution of GRBs.
