Radio Plateaus in Gamma-Ray Burst Afterglows and Their Application in Cosmology

The plateau phase in the radio afterglows has been observed in very few gamma-ray bursts (GRBs), and 27 radio light curves with plateau phase were acquired from the published literature in this article. We obtain the related parameters of the radio plateau, such as temporal indexes during the plateau phase (${\alpha }_1$ and ${\alpha }_2$), break time ($\text{Tbz}$) and the corresponding radio flux ($F_{\mathrm{b}}$). The two parameter Dainotti relation between the break time of the plateau and the corresponding break luminosity ($\text{Lbz}$) in radio band is $\text{Lbz}\propto {\text{Tbz}}^{-1.20\pm 0.24}$. Including the isotropic energy $\text{Eiso}$ and the peak energy $\text{Epi}$, the three parameter correlations for the radio plateaus are written as $\text{Lbz}\propto {\text{Tbz}}^{-1.01\pm 0.24}{\text{Eiso}}^{0.18\pm 0.09}$ and $\text{Lbz}\propto {\text{Tbz}}^{-1.18\pm 0.27}{\text{Epi}}^{0.05\pm 0.28}$, respectively. The correlations are less consistent with that of X-ray and optical plateaus, implying that radio plateaus may have a different physical mechanism. The typical frequencies crossing the observational band may be a reasonable hypothesis that causes the breaks of the radio afterglows. We calibrate GRBs empirical luminosity correlations as standard candle for constraining cosmological parameters, and find that our samples can constrain the flat $\mathrm{\Lambda }$CDM model well, while are not sensitive to non-flat $\mathrm{\Lambda }$CDM model. By combining GRBs with other probes, such as SN and CMB, the constraints on cosmological parameters are $\text{om}=0.297\pm 0.006$ for the flat $\mathrm{\Lambda }$CDM model and $\text{om}=0.283\pm 0.008$, $\text{oL}=0.711\pm 0.006$ for the non-flat $\mathrm{\Lambda }$CDM model, respectively.