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It has been found that the geometrical diagnostic methods can break the degeneracy for dark energy models. In this paper, we investigate the $Om$ diagnostic, the statefinder hierarchy $S_{n}$ and the composite null diagnostic ${S_{n},epsilon}$ for the Tsallis holographic dark energy models with interactions. We find that model parameters and the forms of interaction will influence the values of diagnostic parameters or the trends of the evolutionary trajectories for each model. Moreover, the statefinder hierarchy $S_{3}^{(1)}$ together with ${S_{3}^{(1)},epsilon}$ could give good diagnostic results. Furthermore, we also obtain some issues of cosmological structure by means of the composite null diagnostic.
In order to apply holography and entropy relations to the whole universe, which is a gravitational and thus nonextensive system, for consistency one should use the generalized definition for the universe horizon entropy, namely Tsallis nonextensive e
Using the Tsallis generalized entropy, holographic hypothesis and also considering the Hubble horizon as the IR cutoff, we build a holographic model for dark energy and study its cosmological consequences in the Brans-Dicke framework. At first, we fo
In this work, we analyzed the effect of different prescriptions of the IR cutoffs, namely the Hubble horizon cutoff, particle horizon cutoff, Granda and Oliveros horizon cut off, and the Ricci horizon cutoff on the growth rate of clustering for the T
In this paper, we have examined the R$acute{e}$nyi holographic dark energy (RHDE) model in the framework of an isotropic and spatially homogeneous flat FLRW (Friedmann- Lema$hat i$tre-Robertson-Walker) Universe by considering different values of para
We formulate Barrow holographic dark energy, by applying the usual holographic principle at a cosmological framework, but using the Barrow entropy instead of the standard Bekenstein-Hawking one. The former is an extended black-hole entropy that arise