Fractal Geometry of Higher Derivative Gravity

Becker, Maximilian; Pagani, Carlo; Zanusso, Omar

doi:10.1103/physrevlett.124.151302

Cited by 19 publications

(13 citation statements)

References 60 publications

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“…More general composite operators O ĝ µν can be included in the gravitational EAA[34][35][36][37][38] by coupling them to independent sources[39][40][41][42][43][44][45].Frontiers in Physics | www.frontiersin.org…”

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confidence: 99%

Why the Cosmological Constant Seems to Hardly Care About Quantum Vacuum Fluctuations: Surprises From Background Independent Coarse Graining

Pagani

Reuter

2020

Front. Phys.

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Background Independence is a sine qua non for every satisfactory theory of Quantum Gravity. If one tries to establish a corresponding notion of Wilsonian renormalization, or coarse graining, it presents a major conceptual and technical difficulty usually. In this paper, we adopt the approach of the gravitational Effective Average Action and demonstrate that, generically, coarse graining in Quantum Gravity and in standard field theories on a non-dynamical spacetime are profoundly different. By means of a concrete example, which, in connection with the cosmological constant problem, is also interesting in its own right, we show that the surprising and sometimes counterintuitive implications of Background Independent coarse graining are neither restricted to high energies nor to strongly non-perturbative regimes. In fact, while our approach has been employed in most studies of Asymptotic Safety, this particular ultraviolet behavior plays no essential role in the present context.

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confidence: 99%

Why the Cosmological Constant Seems to Hardly Care About Quantum Vacuum Fluctuations: Surprises From Background Independent Coarse Graining

Pagani

Reuter

2020

Front. Phys.

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“…For instance [25] computed the anomalous dimension γ 0 associated with the d-dimensional volume operator O 0 = d d x √ g. At the NGFP in four dimensions this anomalous dimension turned out to be γ * 0 | d=4 = 3.986 which was taken as a pointer that "spacetime could me much more empty than one would naively expect" [25]. Recently, a similar analysis for Stelle gravity has been reported in [105].…”

Section: Introductionmentioning

confidence: 79%

On the scaling of composite operators in asymptotic safety

Houthoff

Kurov

Saueressig

2020

J. High Energ. Phys.

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The Asymptotic Safety hypothesis states that the high-energy completion of gravity is provided by an interacting renormalization group fixed point. This implies nontrivial quantum corrections to the scaling dimensions of operators and correlation functions which are characteristic for the corresponding universality class. We use the composite operator formalism for the effective average action to derive an analytic expression for the scaling dimension of an infinite family of geometric operators d d x √ gR n . We demonstrate that the anomalous dimensions interpolate continuously between their fixed point value and zero when evaluated along renormalization group trajectories approximating classical general relativity at low energy. Thus classical geometry emerges when quantum fluctuations are integrated out. We also compare our results to the stability properties of the interacting renormalization group fixed point projected to f (R)-gravity, showing that the composite operator formalism in the single-operator approximation cannot be used to reliably determine the number of relevant parameters of the theory.

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“…The higher derivative theories have been very useful in gravity [35], cosmology [36,37], and fractals [38] and have been used by many authors despite the existence of the Ostrogradski instability. To remove this instability, various attempts were made but none of them were a complete success due to the inherent conditions while developing the theory.…”

Section: Discussionmentioning

confidence: 99%

Removal of instabilities of the higher derivative theories in the light of antilinearity

2021

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Theories with higher derivatives involve linear instabilities in the Hamiltonian commonly known as Ostrogradski ghosts and can be viewed as a very serious problem during quantization. To cure this, we have considered the properties of antilinearity that can be found inherently in the non-Hermitian Hamiltonians. Owing to the existence of antilinearity, we can construct an operator, called the V-operator, which acts as an intertwining operator between the Hamiltonian and its Hermitian conjugate. We have used this V-operator to remove the linear momentum term from the higher derivative Hamiltonian by making it non-Hermitian in the first place via an isospectral similarity transformation. The final form of the Hamiltonian is free from the Ostrogradski ghosts under some restriction on the mass term.

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Fractal Geometry of Higher Derivative Gravity

Cited by 19 publications

References 60 publications

Why the Cosmological Constant Seems to Hardly Care About Quantum Vacuum Fluctuations: Surprises From Background Independent Coarse Graining

Why the Cosmological Constant Seems to Hardly Care About Quantum Vacuum Fluctuations: Surprises From Background Independent Coarse Graining

On the scaling of composite operators in asymptotic safety

Removal of instabilities of the higher derivative theories in the light of antilinearity

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