On a Non-linear Interacting New Holographic Dark Energy Models: observational constraints.

In this paper, we study interacting DGP braneworld Holographic Dark Energy model in a spatially flat FRW universe. Mainly, in this study we concentrate our attention on 4 different forms of non linear non-gravitational interaction. The study shows that the equation of state and the deceleration parameter depict an accelerated universe for all variety of interactions. On the other hand, the StateFinder analysis of all models shows that all models behave similar to both quintessence and phantom dark energy, but for their present value only the first model with $3bH(\rho_D+\rho_D^2/(\rho_D+\rho_m))$ interaction term obeys the behavior of phantom dark energy. Moreover, the result of $Om$-diagnostic is an emphasis on the result of the equation of state showing that the current model has a Phantom-like behavior. By the use of the squared sound speed $v^2_s$ we find that the present model is stable compared to the other holographic models of dark energy such as Ghost Dark Energy (GDE), Standard Holographic Dark Energy (HDE), Sharma-Mittal Hologrphic Dark Energty (SMHDE) and Agegraphic Dark Energy (ADE) which are instable against the background perturbation. In order to obtain the best fit values of the parameters in this work we used the latest observational data (cJLA, Boss DR12, Planck 2015, OHD, SGL) implementing Metropolis-Hastings algorithm with $1\sigma$ and $2\sigma$ confidental levels. For choosing the best model we employ Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). We conclude that the proposed model in the presence of the interaction $3bH(\rho_D+\rho_D^2/(\rho_D+\rho_m))$ is compatible with the recent observational data. We obtain the extra density of DGP and braneworld $\Omega_{rc}$ less than 0.003 which has suitable compatibility with the amount of dark components of the universe. Using the modified version of the Einsten-Boltzmann CAMB code...