Tsallis holographic dark energy model with event horizon cutoff in modified gravity

Abstract

We considered the Tsallis holographic dark energy model in frames of Nojiri-Odintsov gravity with $f(R)=R+\lambda R^2-\sigma{\mu}/{R}$. For IR cutoff event horizon is taken. The cosmological evolution of such universe is investigated for various initial conditions and values of parameters. The dependence of the Hubble parameter $H$ from time in the future has an oscillations. It is shown that for $\mu \neq 0$ appearance of singularities are typical and the time up to these singularities can be relatively small from cosmological viewpoint. The singularity is associated with the zero of second deribative of $f(R)$ on $R$. It is interesting to note that these models can describe observational data from Ia supernovae astrophysics and dependence of the Hubble parameter from redshift $z$ at least not worse than canonical $\Lambda$CDM model.