  We compute the late-time correlation functions on three-dimensional de Sitter
spacetime for a higher-spin gravity theory. For this, we elaborate on the
formulation to obtain the wave functional of universe from a dual conformal
field theory, which is used to compute the late-time correlation functions. We
argue that the relation to direct bulk Feynman diagram computations in the
in-in formulation. We furthermore provide a precise prescription to construct a
higher-spin dS$_3$ holography as an analytic continuation of
Gaberdiel-Gopakumar duality for AdS$_3$. Part of results here were already
reported in an earlier letter. We explain the details of their derivations and
extend the analysis to more generic cases in this paper. Previously, we have
examined two- and three-point functions and a simple four-point correlator at
the leading order in Newton constant. Here we also evaluate more complicated
four-point correlators. Finally, we study late-time correlators in an
alternative limit of dS$_3$/CFT$_2$ with critical level coset, such as,
two-point correlator on conical defect geometry. We also examine one-loop
corrections to two-point correlator on dS$_3$.
