Solving the inverse cosmological calibration problem of gamma-ray bursts

Abstract

We have received a new physical characteristics fitting based on actual observational data from the Swift mission's long-duration gamma-ray bursts (LGRBs). We considered such characteristics as the Amati parameters for linear correlation ($E_{\text{iso}}-E_{\text{p},i}$) and the $k$-correction for gravitational lensing and Malmquist bias (GLMB) effect. We used the Pantheon SN Ia catalogue and the standard $\Lambda$CDM model with a fixed Hubble constant of $H_0=70$ km/s/Mpc as the baseline for the Hubble function $\mu (z)$. In our paper, we formulated the inverse cosmological calibration problem (ICCP) in the non-parametric statistics framework. The ICCP involves fitting non-observable physical characteristics while assuming a fixed cosmological model. To solve this problem, we developed a new method that is resistant to non-Gaussian processes. This method is based on error propagation through the Monte Carlo method and the Theil-Sen method for linear regression estimate. We have demonstrated the stability and robustness of this assessment method. The parameter estimates are as follows: $a=0.92_{-0.12}^{+0.12}$, $b=50.32_{-0.32}^{+0.33}$ without considering the GLMB effect, and $a=0.63_{-0.14}^{+0.13}$, $b=50.12_{-0.31}^{+0.33}$, and $k=1.98_{-0.24}^{+0.25}$ with the effect included. The proposed method can be applied to any other calibration sample of known standard candles, a calibrated sample of LGRBs, and the Hubble function $\mu (z)$. In the future, the ICCP idea can be used as an alternative cosmological test for estimating cosmological parameters, including the GLMB effect, or even for the selection of models, providing new information about the Universe. This can be done by analysing the residual values of observational data within the Bayesian statistics paradigm.

arXiv comment19 pages, 6 figures, 6 tables, MNRAS accepted

References in corpus (26)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• The Pantheon+ Analysis: Cosmological Constraints
• Intrinsic spectra and energetics of BeppoSAX Gamma-Ray Bursts with known redshifts
• GRB Formation Rates inferred from the Spectral Peak Energy - Luminosity Relation
• The collimation--corrected GRB energies correlate with the peak energy of their $\nu F_{\nu }$ spectrum
• New Parallaxes of Galactic Cepheids from Spatially Scanning the Hubble Space Telescope: Implications for the Hubble Constant
• The Expansion of the Universe is Faster than Expected
• Measuring the cosmological parameters with the Ep,i-Eiso correlation of Gamma-Ray Bursts
• The THESEUS space mission concept: science case, design and expected performances
• Cosmology with gamma-ray bursts: I. The Hubble diagram through the calibrated $E_{\mathrm{p},\mathrm{i}}$ - $E_{\mathrm{iso}}$ correlation
• Tension with the flat ΛCDM model from a high redshift Hubble Diagram of supernovae, quasars and gamma-ray bursts
• Addressing the circularity problem in the $E_{\text{p}}-E_{\text{iso}}$ correlation of Gamma-Ray Bursts
• 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
• Measuring cosmological parameters with Gamma-Ray Bursts
• Confirming the gamma-ray burst spectral-energy correlations in the era of multiple time breaks
• The updated luminosity correlations of gamma-ray bursts and cosmological implications
• The Linearity of the Cosmic Expansion Field from 300 to 30,000 km/s and the Bulk Motion of the Local Supercluster with Respect to the CMB
• High Redshift Long Gamma-Ray Bursts Hubble Diagram as a Test of Basic Cosmological Relations
• Gamma-ray burst cosmology: Hubble diagram and star formation history
• Distant foreground and the Planck-derived Hubble constant
• A crucial test of the phantom closed cosmological model
• THESEUS$-$BTA cosmological tests using Multimessenger Gamma-Ray Bursts observations
• The Hubble Diagram: Jump from Supernovae to Gamma-Ray Bursts