Wavefunction of the Universe considering all possible boundaries?

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Are there any models or theories of "many worlds/histories" that consider a sum over all possible boundary conditions?
The Hawking-Hartle no boundary condition is well known. The authors considered a many worlds/histories model considering a sum over all compact euclidean metrics.

But are there any models or theories that consider a sum over all possible metrics or boundaries?

And finally, if all possible boundaries are considered, does it mean that the different worlds/histories considered in the model would be described by radically different fundamental laws of physics?
 
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No, there are no models or theories that consider a sum over all possible metrics or boundaries. The Hawking-Hartle no boundary condition does not consider the sum of all possible metrics or boundaries, but instead assumes that the universe obeys the same fundamental laws of physics everywhere. This means that the different worlds/histories considered in the model will be described by the same fundamental laws of physics.