Reconstructing Gamma Ray Burst Energy Relations with Observational H(z) data in Neural Network Framework

TL;DR

A model independent calibration of GRB luminosity relations using observational Hubble parameter H(z) data from the A220 and J220 compilations, thereby avoiding explicit cosmological assumptions and implementing a Bayesian Neural Network framework as an alternative approach.

Abstract

Gamma ray bursts (GRBs) offer a powerful probe of the cosmic expansion history far beyond the redshift range accessible to Type Ia supernovae. However, the calibration of GRB luminosity correlations is hindered by the circularity problem, which arises from assuming a fiducial cosmological model during calibration. In this work, we perform a model independent calibration of GRB luminosity relations using observational Hubble parameter H(z) data from the A220 and J220 compilations, thereby avoiding explicit cosmological assumptions. We employ Artificial Neural Network (ANN) to reconstruct the calibration relation directly from the data. In addition, we implement a Bayesian Neural Network (BNN) framework as an alternative approach, enabling a data driven treatment of both statistical and systematic uncertainties. The calibrated GRB sample is used to constrain the Amati relation, and we systematically compare the outcomes obtained from different calibration techniques and datasets. While the Amati Parameters obtained from GRBs caibrated from the ANN and BNN results are consistent with previous low redshifts calibrations using model-independent methods, the BNN approach provides a more robust framework.

Figures (12)

• Figure 1: Study of Risk with variation of Neurons
• Figure 3: Study of RISK function with variation of Training Iterations
• Figure 4: ANN with 100 Bootstrap Samples
• Figure 5: Hubble Parameter Reconstruction using Artificial Neural Network with uncertainty intervals
• Figure 6: Hubble Parameter Reconstruction using Bayesian Neural Network with uncertainty intervals