Features of the Partition Function of a $Λ>0$ Universe
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| Format: | Preprint |
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2025
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| _version_ | 1866918152783265792 |
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| author | Anninos, Dionysios Baracco, Chiara Brian, Samuel Denef, Frederik |
| author_facet | Anninos, Dionysios Baracco, Chiara Brian, Samuel Denef, Frederik |
| contents | We consider properties of the gravitational path integral, ${Z}_{\text{grav}}$, of a four-dimensional gravitational effective field theory with $Λ>0$ at the quantum level. To leading order, ${Z}_{\text{grav}}$ is dominated by a four-sphere saddle subject to small fluctuations. Beyond this, ${Z}_{\text{grav}}$ receives contributions from additional geometries that may include Einstein metrics of positive curvature. We discuss how a general positive curvature Einstein metric contributes to ${Z}_{\text{grav}}$ at one-loop level. Along the way, we discuss Einstein-Maxwell theory with $Λ>0$, and identify an interesting class of closed non-Einstein gravitational instantons. We provide a detailed study for the specific case of $\mathbb{C}P^2$ which is distinguished as the saddle with second largest volume and positive definite tensor eigenspectrum. We present exact one-loop results for scalar particles, Maxwell theory, and Einstein gravity about the Fubini-Study metric on $\mathbb{C}P^2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_11330 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Features of the Partition Function of a $Λ>0$ Universe Anninos, Dionysios Baracco, Chiara Brian, Samuel Denef, Frederik High Energy Physics - Theory General Relativity and Quantum Cosmology We consider properties of the gravitational path integral, ${Z}_{\text{grav}}$, of a four-dimensional gravitational effective field theory with $Λ>0$ at the quantum level. To leading order, ${Z}_{\text{grav}}$ is dominated by a four-sphere saddle subject to small fluctuations. Beyond this, ${Z}_{\text{grav}}$ receives contributions from additional geometries that may include Einstein metrics of positive curvature. We discuss how a general positive curvature Einstein metric contributes to ${Z}_{\text{grav}}$ at one-loop level. Along the way, we discuss Einstein-Maxwell theory with $Λ>0$, and identify an interesting class of closed non-Einstein gravitational instantons. We provide a detailed study for the specific case of $\mathbb{C}P^2$ which is distinguished as the saddle with second largest volume and positive definite tensor eigenspectrum. We present exact one-loop results for scalar particles, Maxwell theory, and Einstein gravity about the Fubini-Study metric on $\mathbb{C}P^2$. |
| title | Features of the Partition Function of a $Λ>0$ Universe |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.11330 |