Theoretical limits of holographic quintessence

The holographic dark energy model is one of the important ways for dealing with the dark energy problems in the quantum gravity framework. In this model, the dimensionless parameter $c$ plays an essential role in determining the evolution of the holographic dark energy. In particular, the holographic dark energy with $c\geq 1$ can be effectively described by a quintessence scalar-field. However, according to the requirement of the weak gravity conjecture the variation of the quintessence scalar-field should be less than the Planck mass, which would give theoretic constraints on the parameters $c$ and $\Omega_{\mathrm{m0}}$. Therefore, we get the possible theoretical limits on the parameter $c$ for the holographic quintessence model.