Holographic dark energy models with statefinder diagnostic in modified $f(R,T)$ gravity

We study non-viscous and viscous holographic dark energy models for a homogeneous and isotropic flat Friedmann-Robertson-Walker Universe in $f(R,T)$ gravity. We find that the Hubble horizon as an IR cut-off is suitable for both the models to explain the recent accelerated expansion of the Universe. The cosmological parameters like deceleration parameter and statefinder parameters are discussed in each model. In non-viscous model a constant deceleration parameter is found which shows that there is no phase transition. The constraints on the parameters are obtained to analyse the fixed point values of statefinder parameters of SCDM and $Λ$CDM models. We know that the phase transition is required to explain the accelerated expansion of the Universe and this is possible if both the parameters would be time-dependent. Therefore, we extend our analysis to viscous holographic dark energy model to investigate whether this viscous model with the same IR cut-off could be helpful to find the phase transition. We find that this model gives a time-dependent deceleration parameter which achieves a smooth phase transition of the Universe. We also find the time-varying statefinder pair which matches with $Λ$CDM model. We plot the trajectories in $r-s$ and $r-q$ plans to discriminate our model with the existing dark energy models and obtain the quintessence like behaviour for the suitable values of parameters.