Cosmology of the interacting Tsallis holographic dark energy in $f(R,T)$ gravity framework

Abstract

In this work, we have analyzed the cosmology of the Tsallis holographic dark energy (THDE), a particular case of Nojiri-Odintsov HDE proposed in [S. Nojiri and S. D. Odintsov, \textit{Gen. Relativ. Gravit.} \textbf{38} (2006), 1285; \textit{Eur. Phys. J. C} \textbf{77} (2017) 528], using Hubble's horizon cutoff in $f(R,T)=\mu R+\nu T$ model considering pressureless dark matter. We have examined the equation of state (EoS) parameters in this scenario. The deceleration parameter has been evaluated for this interacting model to justify the late-time acceleration of the expanding universe. We have also studied the cosmological consequences of Statefinder pair, $O_{m}(z)$ diagnostics, $r-q$ plane, and $w_{DE}-w^{'}_{DE}$ pair for interacting THDE in $f(R,T)=\mu R+\nu T$ model. We have also illustrated the cosmology of the interacting THDE using Hubble's horizon cutoff in $f(R,T)=R+\gamma R^2+\xi T$ model. The EoS parameter, deceleration parameter and Statefinder pair are studied in this interacting scenario. Attainment of $\Lambda$CDM fixed point has been observed for both models. We have also constrained model parameters based on observational data sets through the formalism of $\chi^{2}$ minimum test.