Holographic temperature bound in the slow-roll inflation

Abstract

We investigate the relationship between the holographic temperature bound and the slow-roll inflation. For this purpose we introduce the holographic temperature bound for a radiation matter :$T\ge T_{\mathrm{H}}$. Here $T_{\mathrm{H}}$ is the Hubble temperature which arises from the cosmological holographic description of for a radiation-dominated universe. For the quasi-de Sitter phase of slow-roll inflation, we find that the holographic temperature bound of $T_{\mathrm{GH}}\ge T_{\mathrm{H}}$ is guaranteed with the Gibbons-Hawking temperature $T_{\mathrm{GH}}$. When $T_{\mathrm{GH}}=T_{\mathrm{H}}$, inflation ends.

9 pages, 1figure