Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation

Reuter, Martin; Saueressig, Frank

doi:10.1103/physrevd.65.065016

Cited by 458 publications

(780 citation statements)

References 31 publications

(1 reference statement)

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“…It is sufficient to retain the terms proportional to √ g and √ gR from the derivative expansion of the traces Tr exp(· · · ) appearing in (8). They can be obtained straightforwardly by means of standard heat kernel techniques.…”

Section: The β-Functions Of G and λmentioning

confidence: 99%

“…We have calculated the non-trivial fixed point (g * , λ * ) = 0 in d = 4, implied by the simultaneous vanishing of β g and β λ in (15), and the critical exponents θ ′ , θ ′′ [3,4] nonuniversal coordinates λ * and g * show a significant m-dependence, and it is impressive to see how this m-dependence cancels out in the product λ * g * which is universal in an exact calculation [4]. For every value of m, the stability matrix (−∂ i β j ), i, j ∈ {g, λ}, has a pair of complex conjugate eigenvalues θ ′ ± iθ ′′ .…”

Section: Universal Quantitiesmentioning

confidence: 99%

“…Most of the existing RG calculations were performed within the framework of the exact RG equation pertaining to the effective average action [18,19,20], applied to a truncated space of action functionals (theory space). It turned out that the UV fixed point necessary for asymptotic safety does indeed exist within the Einstein-Hilbert [3,4,6] and the R 2 -truncation [5], and detailed analyses of the reliability of those approximations [3,5] revealed that the fixed point found is unlikely to be a truncation artifact. But clearly it is necessary to collect further evidence for its existence at the exact level, both within the effective average action formalism (by generalizing the truncation) and with conceptually independent methods.…”

Section: Introductionmentioning

confidence: 99%

“…Recently a lot of work went into the exploration of the Wilsonian renormalization group (RG) flow of Quantum Einstein Gravity [1,2,3,4,5,6,7,8,9] and its possible impact on black holes and cosmology [10,11,12,13,14,15,16]. By definition, Quantum Einstein Gravity (QEG) is the conjectured quantum field theory of the spacetime metric whose bare action is (infinitesimally close to) an ultraviolet (UV) attractive non-Gaussian fixed point of the RG flow.…”

Section: Introductionmentioning

confidence: 99%

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Proper Time Flow Equation for Gravity

Bonanno¹,

Reuter²

2005

J. High Energy Phys.

115

114

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We analyze a proper time renormalization group equation for Quantum Einstein Gravity in the Einstein-Hilbert truncation and compare its predictions to those of the conceptually different exact renormalization group equation of the effective average action. We employ a smooth infrared regulator of a special type which is known to give rise to extremely precise critical exponents in scalar theories. We find perfect consistency between the proper time and the average action renormalization group equations. In particular the proper time equation, too, predicts the existence of a non-Gaussian fixed point as it is necessary for the conjectured nonperturbative renormalizability of Quantum Einstein Gravity.

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Section: The β-Functions Of G and λmentioning

confidence: 99%

Section: Universal Quantitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Proper Time Flow Equation for Gravity

Bonanno¹,

Reuter²

2005

J. High Energy Phys.

115

114

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show abstract

“…(iii) Are renormalization-group methods a viable way to do non-perturbative quantum gravity [88,11], after the recent discovery of a non-Gaussian ultraviolet fixed point [71,89,72] of the renormalization-group flow?…”

Section: Open Problemsmentioning

confidence: 99%

Quantum Gravity: Unification of Principles and Interactions, and Promises of Spectral Geometry

Booss-Bavnbek¹

2007

SIGMA

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Abstract. Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental interactions, while giving rise to new developments in modern mathematics. It is however unclear whether it will ever become a falsifiable physical theory, since it deals with Planck-scale physics. Reviewing a wide range of spectral geometry from index theory to spectral triples, we hope to dismiss the general opinion that the mere mathematical complexity of the unification programme will obstruct that programme.

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Constant‐Roll Inflation in the Generalized SU(2) Proca Theory

et al. 2022

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The generalized SU(2) Proca theory (GSU2P) is a variant of the well known generalized Proca theory where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non-Abelian character and new configurations of the vector field resulting in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the 2D phase space of the system that results when the cosmic triad configuration is employed in the Friedmann-Lemaitre-Robertson-Walker background and find an attractor curve whose attraction basin both covers almost all the allowed region and does not include a Big-Bang singularity. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2) it is constant-roll including, as a limiting case, the slow-roll variety, 3) a number of e-folds N > 60 is easily reached, 4) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein-Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second-order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties that could be found in this scenario when the coupling constants be replaced by general coupling functions and more terms be discovered in the GSU2P.

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Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation

Cited by 458 publications

References 31 publications

Proper Time Flow Equation for Gravity

Proper Time Flow Equation for Gravity

Quantum Gravity: Unification of Principles and Interactions, and Promises of Spectral Geometry

Constant‐Roll Inflation in the Generalized SU(2) Proca Theory

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