  Twisted supergravity is supergravity in a background where the bosonic ghost
field takes a non-zero value. This is the supergravity counterpart of the
familiar concept of twisting supersymmetric field theories. In this paper, we
give conjectural descriptions of type IIA and IIB supergravity in $10$
dimensions. Our conjectural descriptions are in terms of the closed-string
field theories associated to certain topological string theories, and we
conjecture that these topological string theories are twists of the physical
string theories. For type IIB, the results of arXiv:1505.6703 show that our
candidate twisted supergravity theory admits a unique quantization in
perturbation theory. This is despite the fact that the theories, like the
original physical theories, are non-renormalizable. Although we do not prove
our conjectures, we amass considerable evidence. We find that our candidates
for the twisted supergravity theories contain the residual supersymmetry one
would expect. We also prove (using heavily a result of Baulieu arXiv:1009.3893)
the open string version of our conjecture: the theory living on a brane in the
topological string theory is a twist of the maximally supersymmetric gauge
theory living on the brane in the physical string theory.
