Model independent calibrations of gamma ray bursts using machine learning

Abstract

We alleviate the circularity problem, whereby gamma-ray bursts are not perfect distance indicators, by means of a new model-independent technique based on Bézier polynomials. To do so, we use the well consolidate \textit{Amati} and \textit{Combo} correlations. We consider improved calibrated catalogs of mock data from differential Hubble rate points. To get our mock data, we use those machine learning scenarios that well adapt to gamma ray bursts, discussing in detail how we handle small amounts of data from our machine learning techniques. In particular, we explore only three machine learning treatments, i.e. \emph{linear regression}, \emph{neural network} and \emph{random forest}, emphasizing quantitative statistical motivations behind these choices. Our calibration strategy consists in taking Hubble's data, creating the mock compilation using machine learning and calibrating the aforementioned correlations through Bézier polynomials with a standard chi-square analysis first and then by means of a hierarchical Bayesian regression procedure. The corresponding catalogs, built up from the two correlations, have been used to constrain dark energy scenarios. We thus employ Markov Chain Monte Carlo numerical analyses based on the most recent Pantheon supernova data, baryonic acoustic oscillations and our gamma ray burst data. We test the standard $\Lambda$CDM model and the Chevallier-Polarski-Linder parametrization. We discuss the recent $H_0$ tension in view of our results. Moreover, we highlight a further severe tension over ${\Omega }_m$ and we conclude that a slight evolving dark energy model is possible.

26 pages, 20 figures, 7 tables

References in corpus (17)

• Dynamics of dark energy
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey
• Baryon Acoustic Oscillations in the Lyα forest of BOSS DR11 quasars
• The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts
• A Complete Catalog of Swift GRB Spectra and Durations: Demise of a Physical Origin for Pre-Swift High-Energy Correlations
• A time - luminosity correlation for Gamma Ray Bursts in the X - rays
• Cosmology with gamma-ray bursts: I. The Hubble diagram through the calibrated $E_{\mathrm{p},\mathrm{i}}$ - $E_{\mathrm{iso}}$ correlation
• A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram
• The Epeak-Eiso plane of long Gamma Ray Bursts and selection effects
• Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe
• Gamma-Ray Bursts in $1.8<z<5.6$ Suggest that the Time Variation of the Dark Energy is Small
• Confirming the gamma-ray burst spectral-energy correlations in the era of multiple time breaks
• Peak energy of the prompt emission of long Gamma Ray Bursts vs their fluence and peak flux
• Strong evidence for an accelerating universe
• Model-independent limits and constraints on extended theories of gravity from cosmic reconstruction techniques

Cited by in corpus (3)

• $E_{\mathrm{iso}}$-$E_{\mathrm{p}}$ correlation of gamma ray bursts: calibration and cosmological applications
• Low redshift calibration of the Amati relation using galaxy clusters
• Intermediate redshift calibration of Gamma-ray Bursts and cosmic constraints in non-flat cosmology