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As one of the most energetic and brightest events, gamma-ray bursts (GRBs) have been used as a standard candle for cosmological probe. Based on the relevant features of GRBs light curves, a plateau phase followed a decay phase, we obtain X-ray samples of 31 GRBs and optical samples of 50 GRBs, which are thought to be caused by the same physical mechanism. We standardize GRBs using the two-dimension fundamental plane relation of the rest-frame luminosity of the plateau emission ($L_{b,z}$) and the end time of plateau ($T_{b,z}$) $L_{b,z}-T_{b,z}$, as well as the three-dimension fundamental plane correlation including the peak energy ($E_{p,i}$) $L_{b,z}-T_{b,z}-E_{p,i}$. For the cosmological probes, we consider the $\omega$CDM model in which the dark energy consists of one component, and mainly focus on the $X_1X_2$CDM model in which the dark energy is made up of two independent components. We obtain the constraints on the related parameters of the cosmological models using the type Ia supernovae (SNe Ia) data and selected X-ray and optical samples. For the $X_1X_2$CDM model, we find that the values of the equations of state parameters of two dark energies, $\omega_1$ and $\omega_2$, are very close. We also conduct the comparison between the models using the Bayesian information criterion, and find that the $\omega$CDM model is favoured., Comment: 13 pages, 8 figures and 3 tables, accepted for publication in Astronomy & Astrophysics

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 ($\Tbz$) and the corresponding radio flux ($F_{\rm b}$). The two parameter Dainotti relation between the break time of the plateau and the corresponding break luminosity ($\Lbz$) in radio band is $\Lbz \propto \Tbz^{-1.20\pm0.24}$. Including the isotropic energy $\Eiso$ and the peak energy $\Epi$, the three parameter correlations for the radio plateaus are written as $\Lbz \propto \Tbz^{-1.01 \pm 0.24} \Eiso^{0.18 \pm 0.09}$ and $\Lbz \propto \Tbz^{-1.18 \pm 0.27} \Epi^{0.05 \pm 0.28}$, 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 $\Lambda$CDM model well, while are not sensitive to non-flat ${\Lambda}$CDM model. By combining GRBs with other probes, such as SN and CMB, the constraints on cosmological parameters are $\om = 0.297\pm0.006$ for the flat ${\Lambda}$CDM model and $\om = 0.283\pm0.008$, $\oL = 0.711\pm0.006$ for the non-flat ${\Lambda}$CDM model, respectively., Comment: 16 pages, 6 figures and 6 tables, accepted for publication in ApJ

As one of the most energetic and brightest events, gamma-ray bursts (GRBs) can be treated as a promising probe of the high-redshift universe. Similar to type Ia supernovae (SNe Ia), GRBs with same physical origin could be treated as standard candles. We select GRB samples with the same physical origin, which are divided into two groups. One group is consisted of 31 GRBs with a plateau phase feature of a constant luminosity followed by a decay index of about -2 in the X-ray afterglow light curves, and the other has 50 GRBs with a shallow decay phase in the optical light curves. For the selected GRB samples, we confirm that there is a tight correlation between the plateau luminosity $L_0$, the end time of plateau $t_b$ and the isotropic energy release $E_{\gamma,iso}$. We also find that the $L_0-t_b-E_{\gamma,iso}$ correlation is insensitive to the cosmological parameters and no valid limitations on the cosmological parameters can be obtained using this correlation. We explore a new three-parameter correlation $L_0$, $t_b$, and the spectral peak energy in the rest frame $E_{p,i}$ ($L_0-t_b-E_{p,i}$), and find that this correlation can be used as a standard candle to constrain the cosmological parameters. By employing the optical sample only, we find the constraints of $\Omega_m = 0.697_{-0.278}^{+0.402}(1\sigma)$ for a flat $\Lambda$CDM model. For the non-flat $\Lambda$CDM model, the best-fitting results are $\Omega_m = 0.713_{-0.278}^{+0.346}$, $\Omega_{\Lambda} = 0.981_{-0.580}^{+0.379}(1\sigma)$. For the combination of the X-ray and optical smaples, we find $\Omega_m = 0.313_{-0.125}^{+0.179}(1\sigma)$ for a flat $\Lambda$CDM model, and $\Omega_m = 0.344_{-0.112}^{+0.176}$, $\Omega_{\Lambda} = 0.770_{-0.416}^{+0.366}(1\sigma)$ for a non-flat $\Lambda$CDM model., Comment: Accepted for publication in The Astrophysical Journal, 13 pages, 9 figures and 2 tables

We use a semi-analytic galaxy formation model to study the co-evolution of supermassive black holes (SMBHs) with their host galaxies. Although the coalescence of SMBHs is not important, the quasar-mode accretion induced by mergers plays a dominant role in the growth of SMBHs. Mergers play a more important role in the growth of SMBH host galaxies than in the SMBH growth. It is the combined contribution from quasar mode accretion and mergers to the SMBH growth and the combined contribution from starburst and mergers to their host galaxy growth that determine the observed scaling relation between the SMBH masses and their host galaxy masses. We also find that mergers are more important in the growth of SMBH host galaxies compared to normal galaxies which share the same stellar mass range as the SMBH host galaxies., Comment: 10 pages, 5 figures, version published by RAA