  In three dimensions, Kerr-de Sitter spacetime as a solution of Einstein
gravity with positive cosmological constant has a single cosmological horizon.
The flat-space limit (zero cosmological constant limit) of this spacetime is
well-defined and yields the flat-space cosmological solution which is a
significant spacetime in the context of flat-space holography. In this paper,
we calculate the free energy of this spacetime and compare it with the free
energy of the three-dimensional de Sitter spacetime. We investigate which one
of these two spacetimes will dominate in the semi-classical approximation for
estimating the partition function. It is shown that for the same temperature of
cosmological horizon of two spacetimes this is the de Sitter spacetime which is
always dominant. Hence, contrary to asymptotically flat and asymptotically AdS
spacetimes, there is no phase transition in three dimensional de Sitter
gravity.
