dS/dS and T\bar T*

Quantum gravity in realistic, cosmological spacetimes is well motivated by observations and the structure of stress-energy sources in string theory.  We review and explain new developments in the uplift of the AdS/CFT duality to de Sitter spacetime, known as the dS/dS correspondence.  The $T\bar T$ deformation of a conformal field theory has a dual description as a cutoff $AdS_3$ spacetime, at least at the level of pure 3d gravity.  We generalize this deformation in such a way that it builds up a patch of bulk $dS_3$ spacetime instead.  At each step along the trajectory in the space of $2d$ theories, the theory is deformed by a specific combination of $T\bar T$ and the two-dimensional cosmological constant.   This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge.   We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy.  The talk will also describe work in progress joining the two warped throats, incorporating bulk matter, and assessing the generalization to higher dimensions.