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arXiv · 2204.03043

Time Evolution in Quantum Cosmology

Anne-Katherine Burns·David E. Kaplan·Tom Melia·Surjeet Rajendran
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Abstract

The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained using a gauge fixed path integral, as long as one does not integrate over proper time. Using this gauge fixed action we can construct a Hamiltonian in the coherent - or classical - state basis. We show that by construction the coherent states satisfy the classical dynamical equations of General Relativity. They do not satisfy the Hamiltonian constraint. A consequence of this is that the Wheeler-DeWitt equation should not be satisfied in quantum gravity. Classical states have a natural non-trivial time evolution since they are not eigenstates of the Hamiltonian. A general feature of the unconstrained quantum theory of gravity is the prediction of a pressureless dark matter component of either sign energy density in the classical universe which may lead to novel phenomenology.

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Anne-Katherine Burns, David E. Kaplan, Tom Melia, Surjeet Rajendran. 2022-04-06. Time Evolution in Quantum Cosmology. https://arxiv.org/abs/2204.03043

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