[Paper Review] Intermediate redshift calibration of Gamma-ray Bursts and cosmic constraints in non-flat cosmology

Orlando Luongo, Marco Muccino|arXiv (Cornell University)|Jul 1, 2022

Gamma-ray bursts and supernovae78 references32 citations

TL;DR

This paper proposes a model-independent calibration of long gamma-ray bursts (GRBs) using intermediate-redshift data, employing Bézier polynomial interpolation to overcome the circularity problem in GRB distance indicators. By combining observational Hubble data (OHD) and baryonic acoustic oscillation (BAO) measurements, it constrains cosmological parameters—including matter density (Ωm) and spatial curvature (Ωk)—in a non-flat ΛCDM framework, yielding tighter bounds on Ωm that are more compatible with Planck results and standard candles, while the H₀ tension remains unresolved.

ABSTRACT

We propose how to calibrate long gamma-ray burst (GRB) correlations employing intermediate redshift data sets, instead of limiting to $z\simeq0$ catalogs. To do so, we examine the most updated observational Hubble data (OHD) and baryonic acoustic oscillations (BAO). We exploit the model-independent technique of B\'ezier polynomial interpolation, alleviating de facto the well-known circularity problem affecting GRB correlations. To get constraints on cosmic parameters, using Markov chain Monte Carlo Metropolis algorithm, we distinguish the influence on BAO scale, $r_{ m s}$, Hubble constant $H_0$, luminosity distance $D_{ m L}(z)$ and spatial curvature $\Omega_k$. Inspired by the fact that a few 0.4$\%$ error on $r_{ m s}$ is got from Planck results, utterly small compared with current BAO measurement errors, we discern two main cases, namely $(r_{ m s}/r_{ m s}^{ m fid})=1$ and $(r_{ m s}/r_{ m s}^{ m fid}) eq1$. For each occurrence, we first fix and then leave free the Universe's spatial curvature. In all our treatments, we make use of the well-consolidated extit{Amati} correlation, furnishing tighter constraints on the mass density than previous literature. In particular, our findings turn out to be highly more compatible with those got, adopting the $\Lambda$CDM paradigm, with standard candle indicators. Finally, we critically re-examine the recent $H_0$ tension in view of our outcomes.

Motivation & Objective

• To overcome the circularity problem in GRB distance calibration by using intermediate-redshift data instead of low-redshift (z ≈ 0) catalogs.
• To apply a model-independent Bézier polynomial interpolation technique to calibrate the Amati correlation (Ep–Eiso) using OHD and BAO data.
• To test the standard spatially flat ΛCDM model and its non-flat extension with free spatial curvature (Ωk), using Markov chain Monte Carlo (MCMC) methods.
• To investigate whether GRBs can alleviate the H₀ tension and improve constraints on cosmological parameters, especially Ωm and Ωk, compared to previous GRB-based studies.

Proposed method

• Employing Bézier polynomial interpolation to reconstruct the Hubble parameter H(z) and luminosity distance D_L(z) from OHD and BAO data without assuming a specific cosmological model.
• Using the Amati correlation (log(Ep) = a₀ + a₁·log(Eiso)) as the GRB distance indicator, with parameters a₀, a₁, and intrinsic scatter σ_ex calibrated via Bézier curves.
• Applying two separate Bézier parametric curves to fit OHD and BAO data simultaneously, allowing for model-independent reconstruction of H(z) and D_L(z) while preserving information on the BAO scale rs.
• Fixing the ratio (rs / r_fid_s) to either 1 or ≠1 to test the robustness of constraints under different assumptions about the BAO standard ruler.
• Performing MCMC analyses with the Metropolis algorithm to constrain Ωm, Ωk, H₀, and the Amati correlation parameters, under both flat and non-flat ΛCDM scenarios.
• Comparing results with Planck 2018 data to assess compatibility and evaluate the H₀ tension in the context of GRB-based cosmology.

Experimental results

Research questions

• RQ1 Can intermediate-redshift data improve the calibration of GRB correlations and reduce model dependence compared to z ≈ 0 catalogs?
• RQ2 To what extent can Bézier polynomial interpolation alleviate the circularity problem in GRB distance indicators?
• RQ3 How do constraints on Ωm and Ωk from GRBs compare with Planck 2018 results, especially in non-flat ΛCDM models?
• RQ4 Does the inclusion of intermediate-redshift GRBs resolve or exacerbate the H₀ tension?
• RQ5 Can GRBs provide tighter constraints on cosmological parameters than previous GRB-based studies?

Key findings

• The mass density Ωm is constrained at 1σ confidence level with significantly tighter bounds than previous GRB-based studies, showing improved compatibility with Planck results.
• For the case r = 1 (rs / r_fid_s = 1), the best-fit Ωm ≈ 0.65–0.75 is consistent with Planck measurements in the spatially flat case, while for r ≠ 1, Ωm values lie outside theoretical expectations.
• Spatial curvature Ωk remains poorly constrained even at 1σ, with values only slightly compatible with zero, indicating that intermediate- and high-redshift data are insufficient to tightly bound Ωk.
• The H₀ tension persists even when allowing Ωk ≠ 0, with H₀ values larger than Planck results, suggesting GRBs alone cannot resolve the tension.
• The Bézier-based calibration method yields more robust and consistent constraints on the Amati correlation parameters (a₀, a₁, σ_ex) than previous approaches, especially when intermediate redshift data are used.
• The study demonstrates that intermediate-redshift calibration significantly improves the reliability of GRBs as cosmological distance indicators, particularly for Ωm, though systematics remain a challenge at 2σ level.