  We propose that the state represented by the Nariai black hole inside de
Sitter space is the ground state of the de Sitter gravity, while the pure de
Sitter space is the maximal energy state. With this point of view, we
investigate thermodynamics of de Sitter space, we find that if there is a dual
field theory, this theory can not be a CFT in a fixed dimension. Near the
Nariai limit, we conjecture that the dual theory is effectively an 1+1 CFT
living on the radial segment connecting the cosmic horizon and the black hole
horizon. If we go beyond the de Sitter limit, the "imaginary" high temperature
phase can be described by a CFT with one dimension lower than the spacetime
dimension. Below the de Sitter limit, we are approaching a phase similar to the
Hagedorn phase in 2+1 dimensions, the latter is also a maximal energy phase if
we hold the volume fixed.
