Scrutinizing various phenomenological interactions in the context of holographic Ricci dark energy models

In this paper, we examine two types of interacting holographic dark energy model using Pantheon supernova data, BAO BOSS DR12, CMB Planck 2015, fgas (gas mass fraction) and SZ/Xray (Sunyaev–Zeldovich effect and X-ray emission) data from galaxy clusters (GC). In particular, we considered the Holographic Ricci dark energy and Extended holographic Ricci dark energy models. During this analysis, we considered seven types of phenomenological interaction terms (three linear and four non-linear) $$Q_1=3Hb\left( \rho _{D}+\rho _m\right) $$, $$Q_2=3Hb\rho _{D}$$, $$Q_3=3Hb\rho _{m}$$, $$Q_4=3Hb\left( \rho _{D}+\frac{\rho _{D}^2}{\rho _{D}+\rho _m}\right) $$, $$Q_5=3Hb\left( \rho _{m}+\frac{\rho _{m}^2}{\rho _{D}+\rho _m}\right) $$, $$Q_6=3Hb\left( \rho _{D}+\rho _{m}+\frac{\rho _{D}^2}{\rho _{D}+\rho _m}\right) $$, $$Q_7=3Hb\Big (\rho _{D}+\rho _{m}+\frac{\rho _{m}^2}{\rho _{D}+\rho _m}\Big )$$ respectively. To find the best model we apply Bayesian Inference (BI) and use the $$\Lambda $$CDM as the referring model for comparison. Using the Bayesian Evidence model selection method we note that the $$Q_3$$ and $$Q_5$$ interaction terms are favored by observational data among the other ones. The obtained results also demonstrated that the evidence from the Bayesian inference method against the considered types of holographic Ricci dark energy model is strong since the $$\Lambda $$CDM is considered as the reference model and also the $$\Lambda $$CDM is preferred over the models. We also observed that the values of the deceleration parameter and the transition redshift for all models are compatible with the latest observational data and Planck 2015. In addition, we studied the jerk parameter for all models. Using our modified CAMB code, we observed that the interacting models suppress the CMB spectrum at low multipoles and enhances the acoustic peaks