Model-independent calibration of Gamma-Ray Bursts with neural networks

TL;DR

This work addresses the need for model-independent calibration of GRB luminosity correlations to extend cosmology beyond traditional distance indicators. It introduces an artificial neural network framework that reconstructs a cosmology-free $D_L(z)$ from Pantheon+ and uses it to calibrate the 2D and 3D Dainotti relations for the Platinum GRB sample, avoiding Gaussian-process kernel dependencies. By comparing fixed and nuisance-parameter treatments and incorporating redshift-evolution corrections, the study demonstrates reduced intrinsic scatter and robust calibration across priors, with ANN results showing consistency and complementary behavior relative to Gaussian Processes. Cosmological inferences drawn from the calibrated GRBs indicate that evolution-corrected analyses yield more consistent $H_0$ and $\Omega_m$ constraints, reinforcing GRBs as a viable, model-independent high-redshift probe for precision cosmology.

Abstract

The $Λ$ Cold Dark Matter ($Λ$CDM) cosmological model has been highly successful in predicting cosmic structure and evolution, yet recent precision measurements have highlighted discrepancies, especially in the Hubble constant inferred from local and early-Universe data. Gamma-ray bursts (GRBs) present a promising alternative for cosmological measurements, capable of reaching higher redshifts than traditional distance indicators. This work leverages GRBs to refine cosmological parameters independently of the $Λ$CDM framework. Using the Platinum compilation of long GRBs, we calibrate the Dainotti relations-empirical correlations among GRB luminosity properties-as standard candles through artificial neural networks (ANNs). We analyze both the 2D and 3D Dainotti calibration relations, leveraging an ANN-driven Markov Chain Monte Carlo approach to minimize scatter in the calibration parameters, thereby achieving a stable Hubble diagram. This ANN-based calibration approach offers advantages over Gaussian processes, avoiding issues such as kernel function dependence and overfitting. Our results emphasize the need for model-independent calibration approaches to address systematic challenges in GRB luminosity variability, ultimately extending the cosmic distance ladder in a robust way. By addressing redshift evolution and reducing systematic uncertainties, GRBs can serve as reliable high-redshift distance indicators, offering critical insights into current cosmological tensions.

Figures (13)

• Figure 1: A two-layer ANN architecture is shown, where the input is the redshift of a cosmological parameter $\Upsilon(z)$, and the output is the probability distribution $P(\Upsilon) \sim \mathcal{N}(\mu = \Upsilon(z), \sigma = \sigma_\Upsilon(z))$. The parameters $\mu$ and $\Sigma$ are derived from the output distribution.
• Figure 2: ANN reconstruction of the Pantheon+ SNIa logarithmic $D_L(z)$, $\log_{10} D_L(z)$, as a function of the redshift $(z)$ in the left panel. The right panel shows the covariance matrix between ANN reconstruction of the Pantheon+ SN-Ia $\log_{10} D_L(z)$. The color bar on the right shows the covariance $\text{cov}[\log_{10} D_L(z_i), \, \log_{10} D_L(z_j)]$ at redshifts $z_i$ and $z_j$ respectively.
• Figure 3: Differential distributions of the $L_X(T_a)$ variable of the samples at low-z ($z<2.3$) shown in continuous line and with $z \geq 2.3$ with red dashed line.
• Figure 4: 1D posteriors and 2D contours at 68% and 95% confidence levels (C.L.) for the analysis of the 3D Dainotti relation. The analysis assumes Gaussian priors with an $n$-$\sigma$ progression and applies physical constraints $a < 0$, $b > 0$, and $\sigma_{\rm int} > 0$ in the left panel. Comparison using Gaussian (G.) priors and the corresponding Flat (F.) priors at 3$\sigma$ and 5$\sigma$ in the right panel.
• Figure 5: 1D posteriors and 2D contours at 68% and 95% confidence levels (C.L.) for the analysis of the 2D Dainotti relation. The analysis assumes Gaussian priors with an $n$-$\sigma$ progression and applies physical constraints $a < 0$, and $\sigma_{\rm int} > 0$ in the left panel. Comparison using Gaussian (G.) priors and the corresponding Flat (F.) priors at 3$\sigma$ and 5$\sigma$ in the right panel.