Measuring cosmological parameters with a luminosity-time correlation of gamma-ray bursts

Abstract

Gamma-ray bursts (GRBs), as a possible probe to extend the Hubble diagram to high redshifts, have attracted much attention recently. In this paper, we select two samples of GRBs that have a plateau phase in X-ray afterglow. One is short GRBs with plateau phases dominated by magnetic dipole (MD) radiations. The other is long GRBs with gravitational-wave (GW) dominated plateau phases. These GRBs can be well standardized using the correlation between the plateau luminosity $L_0$ and the end time of plateau $t_b$. The so-called circularity problem is mitigated by using the observational Hubble parameter data and Gaussian process method. The calibrated \ltb ~correlations are also used to constrain $\Lambda$CDM and $w(z)$ = $w_0$ models. Combining the MD-LGRBs sample from Wang et al. (2021) and the MD-SGRBs sample, we find ${\Omega }_m=0.33_{-0.09}^{+0.06}$ and ${\Omega }_{\Lambda }$ = $1.06_{-0.34}^{+0.15}$ excluding systematic uncertainties in the nonflat $\Lambda$CDM model. Adding type Ia supernovae from Pantheon sample, the best-fitting results are $w_0$ = $-1.11_{-0.15}^{+0.11}$ and ${\Omega }_m$ = $0.34_{-0.04}^{+0.05}$ in the $w=w_0$ model. These results are in agreement with the $\Lambda$CDM model. Our result supports that selection of GRBs from the same physical mechanism is crucial for cosmological purposes.

18 pages, 12 figures, 1 table, accepted for publication in MNRAS

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