Features of the Partition Function of a Λ>0 Universe

2025/05/16 by Dionysios Anninos, Chiara Baracco, Anninos, Dionysios +5 · 3 citations
Mathematics · #Advanced Mathematical Theories #Advanced Research in Science and Engineering #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.11330

openalex publication_date 2025/05/16 · openalex created_date 2025/10/20 · openalex updated_date 2026/07/28

Abstract

We consider properties of the gravitational path integral, Z_grav, of a four-dimensional gravitational effective field theory with Λ>0 at the quantum level. To leading order, Z_grav is dominated by a four-sphere saddle subject to small fluctuations. Beyond this, Z_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_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 ℂP² 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 ℂP².

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