Neural networks and standard cosmography with newly calibrated high redshift GRB observations

TL;DR

This paper introduces a novel machine learning method combining RNN and BNN to calibrate high-redshift gamma-ray bursts as cosmological probes, enabling cosmographic analysis up to redshift 10 with minimal assumptions.

Contribution

It develops a new neural network-based calibration technique for GRBs using SNeIa data, extending cosmography to higher redshifts with a minimal assumption framework.

Findings

Successfully calibrated GRBs at z>3.6 using the new method.

Extended cosmographic analysis up to z≈10.

Provided constraints on the Universe's kinematic parameters.

Abstract

Gamma-ray bursts (GRBs) detected at high redshift can be used to trace the cosmic expansion history. However, the calibration of their luminosity distances is not an easy task in comparison to Type Ia Supernovae (SNeIa). To calibrate these data, correlations between their luminosity and other observed properties of GRBs need to be identified, and we must consider the validity of our assumptions about these correlations over their entire observed redshift range. In this work, we propose a new method to calibrate GRBs as cosmological distance indicators using SNeIa observations with a machine learning architecture. As well we include a new data GRB calibrated sample using extended cosmography in a redshift range above $z>3.6$. An overview of this machine learning technique was developed in [1] to study the evolution of dark energy models at high redshift. The aim of the method developed in this work is to combine two networks: a Recurrent Neural Network (RNN) and a Bayesian Neural Network (BNN). Using this computational approach, denoted RNN+BNN, we extend the network's efficacy by adding the computation of covariance matrices to the Bayesian process. Once this is done, the SNeIa distance-redshift relation can be tested on the full GRB sample and therefore used to implement a cosmographic reconstruction of the distance-redshift relation in different regimes. Thus, our newly-trained neural network is used to constrain the parameters describing the kinematical state of the Universe via a cosmographic approach at high redshifts (up to $z\approx 10$), wherein we require a very minimal set of assumptions on the deep learning architecture itself that do not rely on dynamical equations for any specific theory of gravity.