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Standardizing Platinum Dainotti-correlated gamma-ray bursts, and using them with standardized Amati-correlated gamma-ray bursts to constrain cosmological model parameters

We show that the Platinum gamma-ray burst (GRB) data compilation, probing the redshift range $0.553 \leq z \leq 5.0$, obeys a cosmological-model-independent three-parameter fundamental plane (Dainotti) correlation and so is standardizable. While they probe the largely unexplored $z \sim 2.3-5$ part of cosmological redshift space, the GRB cosmological parameter constraints are consistent with, but less precise than, those from a combination of baryon acoustic oscillation (BAO) and Hubble parameter [$H(z)$] data. In order to increase the precision of GRB-only cosmological constraints, we exclude common GRBs from the larger Amati-correlated A118 data set composed of 118 GRBs and jointly analyze the remaining 101 Amati-correlated GRBs with the 50 Platinum GRBs. This joint 151 GRB data set probes the largely unexplored $z \sim 2.3-8.2$ region; the resulting GRB-only cosmological constraints are more restrictive, and consistent with, but less precise than, those from $H(z)$ + BAO data.