# Diagnosing Tsallis Holographic Dark Energy models with interactions

## TL;DR

This paper evaluates the effectiveness of geometrical diagnostic methods in distinguishing interacting Tsallis holographic dark energy models, highlighting the influence of model parameters and interactions on diagnostic outcomes.

## Contribution

It applies multiple diagnostic tools to Tsallis holographic dark energy models with interactions, demonstrating their ability to differentiate models and analyze cosmological structures.

## Key findings

- Model parameters and interactions affect diagnostic trajectories.
- Statefinder hierarchy S3(1) effectively distinguishes models.
- Composite null diagnostic reveals issues in cosmological structure.

## Abstract

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.