2024/12/13 by Carlo Branchina, Vincenzo Branchina, Branchina, C. +5 · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Relativity and Gravitational Theory #Advanced Mathematical Theories and Applications
paper · pdf · doi:10.48550/arxiv.2412.10194
Considering (euclidean) quantum gravity in the Einstein-Hilbert truncation,\nwe calculate the one-loop effective action \Γ1l rm grav using a\nspherical background. Usually, this calculation is performed resorting to\nproper-time regularization within the heat kernel expansion and gives rise to\nquartically and quadratically UV-sensitive contributions to the vacuum energy\n\ρ rm vac= frac\Λ rm cc8\π G, with \Λ rm cc and\nG cosmological and Newton constant, respectively. We show that, if the\nmeasure in the path integral that defines \Γ1l rm grav is correctly\ntaken into account, and the physical UV cutoff \Λ rm cut properly\nintroduced, \ρ rm vac presents only a (mild) logarithmic sensitivity to\n\Λ rm cut. We also consider a free scalar field and a free Dirac\nfield on a spherical gravitational background, and find that the same holds\ntrue even in the presence of matter. These results are found without resorting\nto any supersymmetric embedding of the theory, and shed new light on the\ncosmological constant problem.\n