The Hartle-Hawking state is a proposal concerning the state of the universe prior to the Planck epoch. Hartle-Hawking is essentially a no-boundary proposal that the universe is infinitely finite: that there was no time before the Big Bang because time did not exist before the formation of spacetime associated with the Big Bang and subsequent expansion of the universe in space and time.
James Hartle and Stephen Hawking suggest that if we could travel backward in time toward the beginning of the universe, we would note that quite near what might have otherwise been the beginning, time gives way to space such that at first there is only space and no time. Beginnings are entities that have to do with time; because time did not exist before the Big Bang, the concept of a beginning of the universe is meaningless. According to the Hartle-Hawking proposal, the universe has no origin as we would understand it: the universe was a singularity in both space and time, pre-Big Bang. Thus, the Hartle-Hawking state universe has no beginning, but it is not the steady state universe of Hoyle; it simply has no initial boundaries in time nor space.
In theoretical physics, the Hartle–Hawking state, named after James Hartle and Stephen Hawking, is the wave function of the Universe–a notion meant to figure out how the Universe started–that is calculated from Feynman's path integral.
More precisely, it is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes this wave functional.
It is a functional of the metric tensor defined at a (D-1)-dimensional compact surface, the Universe, where D is the spacetime dimension. The precise form of the Hartle–Hawking state is the path integral over all D-dimensional geometries that have the required induced metric on their boundary. According to the theory time diverged from three state dimension - as we know the time now - after the Universe was at the age of the Planck time.
Such a wave function of the Universe can be shown to satisfy the Wheeler–DeWitt equation.
^ John D. Barrow: The Origin of the Universe
Hawking, S.; Hertog, T.; Reall, H. (2000). "Brane new world". Physical Review D 62 (4): 043501. arXiv:hep-th/0003052. Bibcode 2000PhRvD..62d3501H. doi:10.1103/PhysRevD.62.043501. edit
Hartle, J.; Hawking, S. (1983). "Wave function of the Universe". Physical Review D 28 (12): 2960. Bibcode 1983PhRvD..28.2960H. doi:10.1103/PhysRevD.28.2960. edit
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