In this paper, we calibrate the luminosity relation of gamma-ray bursts (GRBs) by Artificial Neural Networks (ANN) which is employed to analyze the Pantheon+ sample of type Ia supernovae (SNe Ia) in a manner independent of cosmological assumptions. The A219 GRB dataset are used to calibrate the Amati relation (\(E_{ \rm p}\)-\(E_{ \rm iso}\)) at low redshift with the ANN framework, facilitating the construction of the Hubble diagram at higher redshifts. Cosmological models are constrained with GRBs at high-redshift and the latest observational Hubble data (OHD) via a Markov Chain Monte Carlo numerical approach. For the Chevallier-Polarski-Linder (CPL) model within a flat universe, we obtain \(\Omega_{ \rm m} = 0.321^{ +0.078}_{ -0.069}\), \(h = 0.654^{ +0.053}_{ -0.071}\), \(w_0 = -1.02^{ +0.67}_{ -0.50}\), and \(w_a = -0.98^{ +0.58}_{ -0.58}\) at the 1-\(\sigma\) confidence level, which indicating a preference for dark energy with potential redshift evolution (\(w_a \neq 0\)). These findings by using ANN align closely with those derived from GRBs calibrated by using Gaussian Processes.
Categories: astro-ph.CO
