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<p>We study quantum gravity corrections to the no-boundary wavefunction describing a universe with spatial topology <i>S</i><sup>1</sup> × <i>S</i><sup>2</sup>. It has been suggested that quantum effects become increasingly important when the size of the circle is large relative to the sphere. In this paper, we confirm this claim by an explicit four-dimensional one-loop calculation of the gravitational path integral preparing such a state. In the process, we clarify some aspects of the gravitational path integral on complex spacetimes. These quantum corrections play a crucial role in ensuring that the norm of the wavefunction is naturally expressed in terms of a path integral over <i>S</i><sup>2</sup> × <i>S</i><sup>2</sup> at the classical level. We extend some of the analysis to more general spatial topologies, as well as to the inclusion of fermions.</p>

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The wavefunction of a quantum S1 × S2 universe

  • 期刊论文

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  • 发表日期：

    2025年7月15日

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  • Gustavo J. Turiaci,
  • Chih-Hung Wu

摘要

We study quantum gravity corrections to the no-boundary wavefunction describing a universe with spatial topology S1 × S2. It has been suggested that quantum effects become increasingly important when the size of the circle is large relative to the sphere. In this paper, we confirm this claim by an explicit four-dimensional one-loop calculation of the gravitational path integral preparing such a state. In the process, we clarify some aspects of the gravitational path integral on complex spacetimes. These quantum corrections play a crucial role in ensuring that the norm of the wavefunction is naturally expressed in terms of a path integral over S2 × S2 at the classical level. We extend some of the analysis to more general spatial topologies, as well as to the inclusion of fermions.