de Sitter Microstates from $T\bar T+\Lambda_2$ and the Hawking-Page
  Transition
  We obtain microstates accounting for the Gibbons-Hawking entropy in $dS_3$,
along with a subleading logarithmic correction, from the solvable $T\bar
T+\Lambda_2$ deformation of a seed CFT with sparse light spectrum. The
microstates arise as the dressed CFT states near dimension $\Delta=c/6$,
associated with the Hawking-Page transition; they dominate the real spectrum of
the deformed theory. We exhibit an analogue of the Hawking-Page transition in
de Sitter. Appropriate generalizations of the $T\bar T+\Lambda_2$ deformation
are required to treat model-dependent local bulk physics (subleading at large
central charge) and higher dimensions. These results add considerably to the
already strong motivation for the continued pursuit of such generalizations
along with a more complete characterization of $T\bar T$ type theories,
building from existing results in these directions.
