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

The plateau phase in radio afterglows has been observed in very few gamma-ray bursts (GRBs), and in this paper, 27 radio light curves with plateau phases were acquired from the published literature. We obtain the related parameters of the radio plateau, such as temporal indexes during the plateau phase (alpha 1 and alpha 2), break time (T b,z), and the corresponding radio flux (F b). The two-parameter Dainotti relation between the break time of the plateau and the corresponding break luminosity (L b,z) in the radio band is Lb,z proportional to Tb,z-1.20 +/- 0.24 . Including the isotropic energy E gamma,iso and peak energy E p,i, the three-parameter correlations for the radio plateaus are written as Lb,z proportional to Tb,z-1.01 +/- 0.24E gamma,iso0.18 +/- 0.09 and Lb,z proportional to Tb,z-1.18 +/- 0.27Ep,i0.05 +/- 0.28 , respectively. The correlations are less consistent with those of the 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 the GRB empirical luminosity correlations as a standard candle for constraining cosmological parameters and find that our samples can constrain the flat Lambda CDM model well but are not sensitive to the nonflat Lambda CDM model. By combining GRBs with other probes, such as supernovae and the CMB, the constraints on the cosmological parameters are omega m = 0.297 +/- 0.006 for the flat Lambda CDM model and omega m = 0.283 +/- 0.008, omega Lambda = 0.711 +/- 0.006 for the nonflat Lambda CDM model.