  We investigate infrared logarithms in de Sitter space from holographic
perspective. We employ a gravitational Fokker-Planck equation to investigate
the time evolution of the de Sitter entropy $S=\pi/(G_N H^2)$, where $H$ is the
Hubble parameter and $G_N$ is the Newton's constant. Under the Gaussian
approximation, we obtain the dynamical $\beta$ function of $g=1/S$. It is
asymptotically free toward the future. It also possesses the ultraviolet fixed
point indicating that the Universe started the de Sitter expansion at the
Planck scale. The pre-inflation era exists to prepare a special initial
condition for the inflation era as a quantum remnant.
