Consistency of nonlinear interacting ghost dark energy with recent observations

In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. We also extend the analysis to the so called generalized ghost dark energy (GGDE) which $\rho_D=\alpha H+\beta H^2$. The model contains three free parameters as $\Omega_D, \zeta(=\frac{8\pi G \beta}{3})$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa from JLA catalog, Hubble parameter, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the joint analysis indicates that $\Omega_D=0.7192\pm0.0062$, $b^2=0.146^{+0.030}_{-0.026}$ and $\zeta=0.104\pm0.047$ at 1 optimal variance error. For the second interaction, the best fit values at $1\sigma$ confidence are $\Omega_D=0.72091\pm0.0065$, $b^2=0.0395\pm0.0080$ and $\zeta\le0.0173$. According to combination of all observational data sets considered in this paper the best fit values for third non-linearly interacting model are $\Omega_D=0.7287\pm0.0062$, $b^2=0.0109\pm0.0023$ and $\zeta\le0.00764$ at $1\sigma$ confidence interval. Finally we found that the presence of interaction is compatible in mentioned models via current observational data sets.