Features of the Partition Function of a $Λ>0$ Universe

• Main Authors: Anninos, Dionysios, Baracco, Chiara, Brian, Samuel, Denef, Frederik
• Format: Journal Article
• Language: English
• Published: 06.07.2025
• Subjects: Physics - General Relativity and Quantum Cosmology; Physics - High Energy Physics - Theory
• DOI: 10.48550/arxiv.2505.11330

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 $\mathbb{C}P^2$.