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

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 approximate to 10), wherein we require a very minimal set of assumptions on the deep learning arquitecture itself that do not rely on dynamical equations for any specific theory of gravity.

Automated summary

This study proposes a new method to calibrate gamma-ray bursts (GRBs) as cosmological distance indicators using a machine learning architecture with data from Type Ia Supernovae (SNeIa) observations. By combining a Recurrent Neural Network (RNN) and a Bayesian Neural Network (BNN), the network's efficacy is extended by computing covariance matrices. This method can be used to implement a cosmographic reconstruction of the distance-redshift relation in different redshift regimes.