  We initiate a study of subregion dualities, entropy, and redundant encoding
of bulk points in holographic theories deformed by $T \bar T$ and its
generalizations. This includes both cut off versions of Anti de Sitter
spacetime, as well as the generalization to bulk de Sitter spacetime, for which
we introduce two additional examples capturing different patches of the bulk
and incorporating the second branch of the square root dressed energy formula.
We provide new calculations of entanglement entropy (EE) for more general
divisions of the system than the symmetric ones previously available. We find
precise agreement between the gravity side and deformed-CFT side results to all
orders in the deformation parameter at large central charge. An analysis of the
fate of strong subadditivity for relatively boosted regions indicates
nonlocality reminiscent of string theory. We introduce the structure of
operator algebras in these systems. The causal and entanglement wedges
generalize to appropriate deformed theories but exhibit qualitatively new
behaviors, e.g. the causal wedge may exceed the entanglement wedge. This leads
to subtleties which we express in terms of the Hamiltonian and modular
Hamiltonian evolution. Finally, we exhibit redundant encoding of bulk points,
including the cosmological case.
