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Quantum Effects of an Extra Compact Dimension on the Wave Function of the Universe

Guowen Peng·Hongya Liu·Qiuyang Zhang
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Abstract

We extend the direct quantum approach of the standard FRW cosmology from 4D to 5D and obtain a Hamiltonian formulation for a wave-like 5D FRW cosmology. Using a late-time approximation we isolate out a y-part from the full wave function of the 5D Universe. Then we find that the compactness of the fifth dimension y yields a quantized spectrum for the momentum $P_{5}$ along the fifth dimension, and we show that the whole space-part of the wave function of the 5D Universe satisfies a two-dimensional Schrödinger equation.

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Guowen Peng, Hongya Liu, Qiuyang Zhang. 2002-04-10. Quantum Effects of an Extra Compact Dimension on the Wave Function of the Universe. https://arxiv.org/abs/gr-qc/0111062

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