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Gamma-ray burst data strongly favor the three-parameter fundamental plane (Dainotti) correlation relation over the two-parameter one

Gamma-ray bursts (GRBs), observed to redshift $z=9.4$, are potential probes of the largely unexplored $z\sim 2.7-9.4$ part of the early Universe. Thus, finding relevant relations among GRB physical properties is crucial. We find that the Platinum GRB data compilation, with 50 long GRBs (with relatively flat plateaus and no flares) in the redshift range $0.553 \leq z \leq 5.0$, and the LGRB95 data compilation, with 95 long GRBs in $0.297 \leq z \leq 9.4$, as well as the 145 GRB combination of the two, strongly favor the three-dimensional (3D) fundamental plane (Dainotti) correlation relation (between the peak prompt lumininosity, the luminosity at the end of the plateau emission, and its rest frame duration) over the two-dimensional one (between the luminosity at the end of the plateau emission and its duration). The 3D Dainotti correlations in the three data sets are standardizable. We find that while LGRB95 data have $\sim50$% larger intrinsic scatter parameter values than the better-quality Platinum data, they provide somewhat tighter constraints on cosmological-model and GRB-correlation parameters, perhaps solely due to the larger number of data points, 95 versus 50. This suggests that when compiling GRB data for the purpose of constraining cosmological parameters, given the quality of current GRB data, intrinsic scatter parameter reduction must be balanced against reduced sample size.