Different faces of generalized holographic dark energy

Understand

In the formalism of generalized holographic dark energy (HDE), the holographic cut-off is generalized to depend upon $L_\mathrm{IR} = L_\mathrm{IR} \left( L_\mathrm{p}, \dot L_\mathrm{p}, \ddot L_\mathrm{p}, \cdots, L_\mathrm{f}, \dot L_\mathrm{f}, \cdots, a\right)$ with $L_\mathrm{p}$ and $L_\mathrm{f}$ are the particle horizon and the future horizon, respectively (moreover $a$ is the scale factor of the universe).

• Based on such formalism, in the present paper, we show that a wide class of dark energy (DE) models can be regarded as different candidates of the generalized HDE family, with respective cut-offs.
• This can be thought as a symmetry between the generalized HDE and different DE models.
• In this regard, we consider several entropic dark energy models - like Tsallis entropic DE, the R\'{e}nyi entropic DE, and the Sharma-Mittal entropic DE - and showed that they are indeed equivalent with the generalized HDE.