[Paper Review] Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way

Hanbei Xie, Xiaodong Nong+4 more|arXiv (Cornell University)|Jul 31, 2023

Gamma-ray bursts and supernovae4 citations

TL;DR

This paper presents a cosmology-independent method to constrain cosmological models using 221 long gamma-ray bursts (GRBs) and observational Hubble data (OHD), calibrating the Amati relation (Ep–Eiso correlation) via Gaussian process regression on the Pantheon+ SNe Ia sample. It finds Ωm = 0.348⁺⁰.⁰⁴⁸₋⁰.⁰⁶⁶ and h = 0.680⁺⁰.⁰²⁹₋⁰.⁰²⁹ for flat ΛCDM, consistent with simultaneous fitting and low-redshift calibrations, enabling high-redshift cosmology without circularity issues.

ABSTRACT

In this paper, we present a cosmology-independent method to constrain cosmological models from the latest 221 gamma-ray bursts (GRBs) sample, including 49 GRBs from Fermi catalog with the Amati relation (the $E_{ m p}$-${E}_{ m iso}$ correlation), which are calibrated by using a Gaussian process from the Pantheon+ type Ia supernovae (SNe Ia) sample. With 182 GRBs at $0.8\le z\le8.2$ in the Hubble diagram and the latest observational Hubble data (OHD) by the Markov Chain Monte Carlo (MCMC) method, we obtained $Ω_{ m m}$ = $0.348^{+0.048}_{-0.066}$ and $h$ = $0.680^{+0.029}_{-0.029}$ for the flat $Λ$CDM model, and $Ω_{ m m}$ = $0.318^{+0.067}_{-0.059}$, $h$ = $0.704^{+0.055}_{-0.068}$, $w$ = $-1.21^{+0.32}_{-0.67}$ for the flat $w$CDM model. These results are consistent with those in which the coefficients of the Amati relation and the cosmological parameters fitted simultaneously.

Motivation & Objective

• To overcome the circularity problem in GRB-based cosmological constraints by avoiding fiducial cosmological model dependence.
• To calibrate the Amati relation (Ep–Eiso correlation) in a model-independent way using SNe Ia data via Gaussian process regression.
• To constrain cosmological parameters (Ωm, h, w) using high-redshift GRBs (z ≥ 0.8) and 32 OHD data in a cosmology-independent framework.
• To validate the consistency of results between cosmology-independent calibration and simultaneous fitting of GRB relations and cosmological models.
• To prepare for future high-precision constraints using upcoming SVOM mission GRB data with smaller scatter.

Proposed method

• Calibrate the Amati relation (Ep–Eiso correlation) in GRBs using Gaussian process regression on the Pantheon+ SNe Ia sample to avoid fiducial model dependence.
• Construct a GRB Hubble diagram using 221 GRBs from the J221 sample (z = 0.03 to 8.20), including 49 Fermi GRBs, with the calibrated Amati relation.
• Incorporate 32 observational Hubble data (OHD) points from cosmic chronometers to improve parameter constraints.
• Apply the Markov Chain Monte Carlo (MCMC) method to simultaneously constrain cosmological parameters (Ωm, h, w) and GRB relation parameters (a, b, σint).
• Compare results from cosmology-independent calibration with those from simultaneous fitting of GRB relation and cosmological parameters.
• Use Bézier parametric curves and interpolation techniques to model the Hubble parameter evolution, ensuring model-independence.

Experimental results

Research questions

• RQ1 Can the Amati relation in GRBs be calibrated in a cosmology-independent way using SNe Ia data and Gaussian processes?
• RQ2 What are the cosmological constraints (Ωm, h, w) derived from high-redshift GRBs (z ≥ 0.8) and OHD without assuming a fiducial cosmology?
• RQ3 How do the cosmological constraints from cosmology-independent GRB calibration compare with those from simultaneous fitting of GRB relations and cosmological models?
• RQ4 Is the Amati relation in GRBs consistent with redshift evolution, and does it remain valid at z > 8?
• RQ5 To what extent do GRBs and OHD jointly constrain the flat ΛCDM and wCDM models in a model-independent framework?

Key findings

• For the flat ΛCDM model, the cosmology-independent method yields Ωm = 0.348⁺⁰.⁰⁴⁸₋⁰.⁰⁶⁶ and h = 0.680⁺⁰.⁰²⁹₋⁰.⁰²⁹ at 1σ confidence level using 182 GRBs (z ≥ 0.8) and 32 OHD.
• For the flat wCDM model, the constraints are Ωm = 0.318⁺⁰.⁰⁶⁷₋⁰.⁰⁵⁹, h = 0.704⁺⁰.⁰⁵⁵₋⁰.⁰⁶⁸, and w = -1.21⁺⁰.³²₋⁰.⁶⁷ at 1σ, using the same GRB and OHD data.
• The results from cosmology-independent calibration are consistent with those obtained via simultaneous fitting of GRB relation and cosmological parameters.
• The Amati relation coefficients (a ≈ 52.87, b ≈ 1.45) and intrinsic scatter (σint ≈ 0.39) remain stable across different calibration methods and redshift ranges.
• Using 131 GRBs at z ≥ 1.4, the constraints are Ωm = 0.314⁺⁰.⁰⁴⁶₋⁰.⁰⁶³ and h = 0.681⁺⁰.⁰²⁹₋⁰.⁰²⁹ for ΛCDM, showing robustness at high redshift.
• The simultaneous fitting of Ωm, h, w, a, b, and σint yields consistent results: Ωm = 0.395⁺⁰.⁰⁵⁴₋⁰.⁰⁷⁸, h = 0.651⁺⁰.⁰³⁰₋⁰.⁰³⁰, w = -0.97⁺⁰.⁶³₋⁰.³⁰, confirming the reliability of the method.