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arXiv · 2205.08496

A Simple Model for Quantum Gravity I: the one-dimensional case

Ricardo Paszko
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Abstract

We propose and analytically solve a simple Euclidean model for quantum gravity in one dimension. The geometry is parametrized by angles associated with a circle of fixed radius $\ell$, allowing the use of the normalized Haar measure of U(1) and character expansions. In the case of an open curve, the continuum limit is trivial: the size of the universe is infinite, independently of the value of the cosmological constant. In the closed case, however, the continuum limit is nontrivial, resulting in a finite-size universe for positive cosmological constant. The presence of a scalar field slightly modifies this result while preserving its behavior. We also discuss possible generalizations of the model to higher dimensions.

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Ricardo Paszko. 2022-05-17. A Simple Model for Quantum Gravity I: the one-dimensional case. https://arxiv.org/abs/2205.08496

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