The Renormalization Group flow of unimodular f(R) gravity

Abstract

Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological constant is not a coupling in the unimodular action, providing a new vantage point from which to address the cosmological constant fine-tuning problem. Here, a quantum theory based on the asymptotic safety scenario is studied, and evidence for an interacting fixed point in unimodular f(R) gravity is found. We study the fixed point and its properties, and also discuss the compatibility of unimodular asymptotic safety with dynamical matter, finding evidence for its compatibility with the matter degrees of freedom of the Standard Model.

17 pages, 2 figures; new version with some clarifications, identical to version to appear in JHEP

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• Unimodular Gravity vs General Relativity: A status report
• Correlation functions on a curved background
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• The background scale Ward identity in quantum gravity
• Asymptotic solutions in asymptotic safety
• The path integral of unimodular gravity
• Scalar-Tensor theories within Asymptotic Safety
• Gravitational antiscreening in stellar interiors
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• Can quantum fluctuations differentiate between standard and unimodular gravity?
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• Are there ALPs in the asymptotically safe landscape?
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• Scaling solutions for asymptotically free quantum gravity
• Variable $G$ and $\Lambda$ gravity theory and analytical Cosmological Solutions using Noether symmetry approach
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• Fate of chiral symmetry in Riemann-Cartan geometry