2017/02/21 by Jorn Biemans, Alessia Platania, Frank Saueressig · 1 citation
Mathematics · Physics and Astronomy · #Asymptotic safety in quantum gravity #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Fixed point #Gaussian #General relativity #Geometry #Gravitation #Infrared fixed point #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum #Quantum gravity #Quantum mechanics #Renormalization #Renormalization group #Scalar (mathematics) #Scalar field #Thermal quantum field theory #Ultraviolet fixed point #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep05(2017)093
42 pages, 6 figures
arxiv created 2017/02/21 · openalex publication_date 2017/05/01 · arxiv updated 2017/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) “time”- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton’s constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.