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arXiv · 1807.03864

The Universe as an Oscillator

Masooma Ali·Syed Moeez Hassan·Viqar Husain
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Abstract

We apply the idea of using a matter time gauge in quantum gravity to quantum cosmology. For the Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe with dust and cosmological constant $Λ$, we show that the dynamics maps exactly to the simple harmonic oscillator in the dust-time gauge. For $Λ>0$ the oscillator frequency is imaginary, for $Λ<0$ it is real, and for $Λ=0$ the Universe is a free particle. This result provides (i) a simple demonstration of non-perturbative singularity avoidance in quantum gravity for all $Λ$, (ii) an exact Lorentzian Hartle-Hawking wave function, and (iii) gives the present age of the Universe as the characteristic decay time of the propagator.

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Masooma Ali, Syed Moeez Hassan, Viqar Husain. 2018-07-20. The Universe as an Oscillator. https://doi.org/10.1103/physrevd.98.086002

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