Brans–Dicke theory in the local potential approximation

Benedetti, Dario; Guarnieri, Filippo

doi:10.1088/1367-2630/16/5/053051

Cited by 32 publications

(36 citation statements)

References 73 publications

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“…In this work, we used the functional renormalization group equation for the effective average action Γ k , (1.1), to establish the existence of a suitable fixed function in the realm of f (R)-truncations spanned by the ansatz (1.2). The PDE governing the k-dependence of f k (R) was derived for a four-dimensional background sphere where all curvature invariants can be expressed in terms of the scalar curvature R. Despite the vast body of earlier works [56,57,59,68], this is the first time that a suitable fixed function has been found and its construction constitutes an important step towards generalizing finite-dimensional truncations of the gravitational RG flow to approximations containing an infinite number of scale-dependent coupling constants. Our solution is globally well-defined on the positive real axis and its UV-expansion at r = 0 yields a positive cosmological constant and Newton's constant.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Demmel

Saueressig

Zanusso

2015

J. High Energ. Phys.

103

120

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Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory's renormalization group flow. In this work, we use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants. We formulate a list of guiding principles underlying the construction of a partial differential equation encoding the scale-dependence of f (R)-gravity. We show that this equation admits a unique, globally well-defined fixed functional describing the non-Gaussian fixed point at the level of functions of the scalar curvature. This solution is constructed explicitly via a numerical double-shooting method. In the UV, this solution is in good agreement with results from polynomial expansions including a finite number of coupling constants, while it scales proportional to R 2 , dressed up with non-analytic terms, in the IR. We demonstrate that its structure is mainly governed by the conformal sector of the flow equation. The relation of our work to previous, partial constructions of similar scaling solutions is discussed.

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Section: Conclusion and Discussionmentioning

confidence: 99%

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Demmel

Saueressig

Zanusso

2015

J. High Energ. Phys.

103

120

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“…Over the years a series of complementary approaches capable of testing the Asymptotic Safety hypothesis have been developed. Starting from the pioneering work [14], functional renormalization group methods have established the existence of a suitable NGFP in a wide range of approximations , including the demonstration that the NGFP persists in the presence of the perturbative two-loop counterterm [48] and upon including an infinite number of scale-dependent couplings [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. Moreover, a first step connecting the NGFP to the underlying conformal field theory appeared in [64], possible completions of the flow at low energy have been discussed in [17,24,38,40,41] and geometric arguments determining the scaling of Newton's constant at the NGFP have been forwarded in [65,66].…”

Section: Introductionmentioning

confidence: 99%

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

2017

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Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the non-Gaussian fixed points characteristic for Asymptotic Safety the setting exhibits a second family of non-Gaussian fixed points with a positive Newton's constant and real critical exponents. The presence of these new fixed points alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the -expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.

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“…In a complementary approach, the fixed point structure arising within scalar-tensor theory has been studied in [24][25][26][27][28][29][30][31]. 1 This setup includes two arbitrary functions of the scalar field φ, a scale-dependent scalar potential V k (φ) and a function F k (φ) encoding the…”

Section: Jhep12(2017)121mentioning

confidence: 99%

On avoiding Ostrogradski instabilities within Asymptotic Safety

Becker

Ripken

Saueressig

2017

J. High Energ. Phys.

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We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques. The novel feature is the inclusion of higher-derivative terms in the scalar propagator. Such terms give rise to Ostrogradski ghosts which signal an instability of the system and are therefore dangerous for the consistency of the theory. Since it is expected that such terms are generated dynamically by the renormalization group flow they provide a potential threat when constructing a theory of quantum gravity based on Asymptotic Safety. Our work then establishes the following picture: upon incorporating higher-derivative terms in the scalar propagator the flow of the gravity-matter system possesses a fixed point structure suitable for Asymptotic Safety. This structure includes an interacting renormalization group fixed point where the Ostrogradski ghosts acquire an infinite mass and decouple from the system. Tracing the flow towards the infrared it is found that there is a subset of complete renormalization group trajectories which lead to stable renormalized propagators. This subset is in one-to-one correspondence to the complete renormalization group trajectories obtained in computations which do not keep track of the higher-derivative terms. Thus our asymptotically safe gravity-matter systems are not haunted by Ostrogradski ghosts.

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Brans–Dicke theory in the local potential approximation

Cited by 32 publications

References 73 publications

A proper fixed functional for four-dimensional Quantum Einstein Gravity

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

On avoiding Ostrogradski instabilities within Asymptotic Safety

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