Boundary-value problems in RG flows are not always unique when the beta-function Jacobian has complex eigenvalues, unlike initial-value problems, with a diagnostic tool and examples in the SM and ASQG.
Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative $\Fbeta$-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found when using a smooth cutoff. The system of equations with sharp cutoff is then solved numerically, deriving the complete renormalization group flow of the Einstein-Hilbert truncation in $d=4$. The resulting renormalization group trajectories are classified and their physical relevance is discussed. The non-trivial fixed point which, if present in the exact theory, might render Quantum Einstein Gravity nonperturbatively renormalizable is investigated for various spacetime dimensionalities.
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In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
Asymptotically safe gravitational form factors are obtained by integrating the proper-time flow to k=0; finite cutoff-independent results with 1/q² UV decay require selecting the non-Gaussian fixed point as UV boundary condition.
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
Quantum deformation of projective phase-space geometry induces a conformally deformed FLRW metric whose time-dependent corrections modify inflationary background equations, slow-roll parameters, and perturbations in a covariant manner.
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.
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Non-uniqueness of boundary-value problems in Renormalization Group flows
Boundary-value problems in RG flows are not always unique when the beta-function Jacobian has complex eigenvalues, unlike initial-value problems, with a diagnostic tool and examples in the SM and ASQG.
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Towards gauge independence in asymptotically safe quantum gravity
In an essential proper-time scheme, gauge dependence of the flow for Newton's constant cancels order-by-order once redundant off-shell terms are absorbed by field redefinitions, leaving a gauge-independent non-Gaussian fixed point.
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Spectral Functions of Lorentzian Quantum Gravity
Spectral functions for graviton and scalar graviton modes are derived in Lorentzian asymptotically safe quantum gravity via adapted FRG flow equations, yielding normalisable results consistent with infrared effective theory.
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Asymptotically Safe Gravitational Form Factors from the Proper-Time Flow Equation
Asymptotically safe gravitational form factors are obtained by integrating the proper-time flow to k=0; finite cutoff-independent results with 1/q² UV decay require selecting the non-Gaussian fixed point as UV boundary condition.
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Quantum gravity contributions to the gauge and Yukawa couplings in proper time flow
Proper-time flow yields positive gravitational corrections to gauge beta functions and negative leading corrections to Yukawa beta functions at the Einstein-Hilbert fixed point, with quantified scheme dependence and limited room for interactive matter fixed points.
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Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
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Quantum-Deformed Phase-Space Geometry and Emergent Inflation in Effective Four-Dimensional Spacetime
Quantum deformation of projective phase-space geometry induces a conformally deformed FLRW metric whose time-dependent corrections modify inflationary background equations, slow-roll parameters, and perturbations in a covariant manner.
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Asymptotically safe quantum gravity and its phenomenology -- a review
Review surveying progress toward realistic asymptotically safe quantum gravity with quantum scale symmetry and observational implications.