  It has been argued that the entropy of de Sitter space corresponds to the
entanglement between disconnected regions computable by switching on a replica
parameter $q$ modeled by the quotient dS$/\mathbb{Z}_q$. Within this framework,
we show that the centrally-extended asymptotic symmetry algebra near the cosmic
horizon is a single copy of the Virasoro algebra. The resulting density of
states matches the semi-classical result of Gibbons and Hawking up to an
undetermined constant that is chosen to reproduce the entanglement entropy
previously found in the literature. It follows that the logarithmic quantum
corrections to the Cardy entropy reproduces the known one-loop result computed
in the bulk in the presence of a cutoff. The resulting entanglement entropy
follows the divergent area law, where the UV cutoff is now a function of the
replica parameter. Thus, as the near-horizon CFT fixes the cutoff in units of
the Planck scale, the model can be viewed as a probe into whether the defect
Hilbert space has a finite dimension; indeed, the limit $q\to 0$, reproduces
Banks' formula. We also study the quantum corrections of the effective
description of the horizon entropy by means of Liouville field theory, where
the large $q$ limit corresponds to a realization of dS$_3$/CFT$_2$
correspondence matching the logarithmic corrections to three-dimensional de
Sitter space obtained by computing the one-loop contribution to the quantum
gravity partition function in the round three-sphere.
