What is the Hartle-Hawking no-boundary proposal in quantum cosmology?

The no-boundary proposal is a quantum cosmological model that assumes no initial singularity, and involves the notion of imaginary time, which turns the Lorentzian-like relativistic metric into a real Euclidean metric. One can move backward and forward along imaginary time, just as one can move right and left in physical space. In essence, the no-boundary proposal states that the universe is finite but had no initial singularity to produce a boundary.

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