Renormalization Group Flow in Scalar-Tensor Theories. II

Abstract

We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with Functional Renormalization Group techniques. We find UV fixed points where the gravitational couplings have non-trivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in $d=4$ for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we notice that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in $d=4$ including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional.

14 pages. v.2: Minor changes, some references added

References in corpus (20)

• Exact evolution equation for the effective potential
• The Standard Model Higgs boson as the inflaton
• The Effective Field Theory of Inflation
• Effective Field Theory for Inflation
• Power-counting and the Validity of the Classical Approximation During Inflation
• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• On the renormalization group flow of f(R)-gravity
• Gauge singlet scalar as inflaton and thermal relic dark matter
• Fixed points of quantum gravity in extra dimensions
• Renormalization Group Flow in Scalar-Tensor Theories. I
• Cosmological Dark Energy: Prospects for a Dynamical Theory
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• Macroscopic Effects of the Quantum Trace Anomaly
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Conformally reduced quantum gravity revisited
• On fixed points of quantum gravity
• The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
• Fixed points of quantum gravity in higher dimensions

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• Functional renormalization with fermions and tetrads
• Remarks on Higgs Inflation
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
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• On avoiding Ostrogradski instabilities within Asymptotic Safety
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• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
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• Constraints on discrete global symmetries in quantum gravity
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
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• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric