A Test of Amati Relation Using HII Galaxy Distances

We use model-independent luminosity distances of 186 HII galaxy observations to address the circularity problem in the Amati relation for Gamma-ray Bursts (GRBs). For this purpose, we used Artificial Neural Network-based interpolation to reconstruct the luminosity distance corresponding to the GRB redshift. We then use two independent GRB datasets to test the robustness of the Amati relation at redshifts below z=2.6. Our best-fit Amati relation parameters are consistent for the same datasets to within 1σ. The intrinsic scatters which we obtain for the two datasets of about 28% and 35% are comparatively larger. This implies that the Amati relation using HII galaxies as distance anchors cannot be used as a probe of precision cosmology.