Constant-roll inflation driven by holographic dark energy

The scenario of constant-roll inflation is investigated assuming that it is caused by holographic dark energy with energy density $3M_p^2 c^2 / L^2$. The energy density with varying $c$ parameter and Hubble radius as infrared cutoff provides a proper description for the late time acceleration expansion. This motivates us to study the role of the same holographic dark energy in the scenario of constant-roll inflation. One of the main features of constant-roll inflation is that the second slow-roll parameter is constant which is not necessarily small. This feature brings a differential equation for the parameter $c$. After finding an analytical solution for the parameter, the observable parameters are obtained at the time of inflation, and by comparing the model with data, the constants of the model are determined. The energy scale of inflation is estimated which is about $10^{16} \; {\rm GeV}$. Finally, a correspondence between the HDE and canonical scalar field is considered and the behavior of the constructed potential and its magnitude is discussed.