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- Wavefunction of the Universe Circa the Beginning (and its past & future)

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18070042

I will first outline an effective field theory for cosmology (EFTC) that is based on the Standard Model coupled to General Relativity and improved with Weyl symmetry. Any version of quantum gravity (QG), including string theory, must include the same improvement, otherwise QG will not be geodesically complete. Based on arguments of an underlying QG theory, this effective field theory banishes higher curvature terms in the action, thus making this EFTC mathematically sufficiently well behaved to make unique predictions for the classical solutions and the quantum wavefunction at the singularity, as well as past the singularity, for a complete cosmology that includes the past, future and detailed quantitative solution at the big bang.

Using this EFTC, I will show its predictions of surprising behavior of the universe at the singularity that cosmologists usually "conveniently" ignore, but they should not, because this predicts the initial conditions. I will illustrate this behavior with detailed formulas and plots of the classical and quantum solutions. The solutions are given in the geodesically complete mini-superspace that has the flavor of the extended spacetime of a black hole or extended Rindler spacetime. The analytic continuation of the quantum wavefunction across the horizons describes the passage through the singularities. The mathematical solution of this analytic continuation solves a long-standing problem of the singular 1/r^2 potential in quantum mechanics that dates back to Von-Neumann. The analytic properties of the wavefunction also reveals an infinite stack of universes sewn together at the horizons of the geodesically complete space. Remaining open questions and problems will be outlined.

©2012 Perimeter Institute for Theoretical Physics