Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy

TL;DR

This study uses updated gamma-ray burst and supernova data to constrain cosmological models, finding results consistent with the standard Lambda Cold Dark Matter model and exploring alternative dark energy parametrizations.

Contribution

It introduces an updated calibration of GRB luminosity relations and applies them to constrain the Cardassian expansion and dark energy models using high-redshift data.

Findings

Adding high-z GRBs improves constraints on cosmological parameters.

Best-fit parameters for the Cardassian model are consistent with Lambda CDM.

Universe's behavior up to z=8.2 aligns with the concordance model.

Abstract

We update gamma-ray burst (GRB) luminosity relations among certain spectral and light-curve features with 139 GRBs. The distance modulus of 82 GRBs at $z>1.4$ can be calibrated with the sample at $z\leq1.4$ by using the cubic spline interpolation method from the Union2.1 Type Ia supernovae (SNe Ia) set. We investigate the joint constraints on the Cardassian expansion model and dark energy with 580 Union2.1 SNe Ia sample ($z<1.4$) and 82 calibrated GRBs data ($1.4<z\leq8.2$). In $\Lambda$CDM, we find that adding 82 high-\emph{z} GRBs to 580 SNe Ia significantly improves the constrain on $\Omega_{m}-\Omega_{\Lambda}$ plane. In the Cardassian expansion model, the best fit is $\Omega_{m}= 0.24_{-0.15}^{+0.15}$ and $n=0.16_{-0.52}^{+0.30}$ $(1\sigma)$, which is consistent with the $\Lambda$CDM cosmology $(n=0)$ in the $1\sigma$ confidence region. We also discuss two dark energy models in which the equation of state $w(z)$ is parametrized as $w(z)=w_{0}$ and $w(z)=w_{0}+w_{1}z/(1+z)$, respectively. Based on our analysis, we see that our Universe at higher redshift up to $z=8.2$ is consistent with the concordance model within $1\sigma$ confidence level.