Asymptotic Safety, Fractals, and Cosmology

Reuter, Martin; Saueressig, Frank

doi:10.1007/978-3-642-33036-0_8

Cited by 61 publications

(67 citation statements)

References 159 publications

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“…Asymptotic safety (depending on the operators assumed in the action) and multifractional models (depending on their construction) are two instances. CDT show only two regimes but the small-scale one is probably an intermediate, not a deep UV feature of the model [44].…”

Section: Universality Robustness and Uniquenessmentioning

confidence: 85%

Diffusion in multiscale spacetimes

Calcagni

2013

Phys. Rev. E

140

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We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples, and the most general spectral-dimension profile of multifractional spaces is constructed.

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Section: Universality Robustness and Uniquenessmentioning

confidence: 85%

Diffusion in multiscale spacetimes

Calcagni

2013

Phys. Rev. E

140

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“…We focus on an asymptotically safe model of quantum gravity [4]. Based on the groundbreaking work of Reuter [5], compelling evidence for the existence of an asymptotically safe fixed point in pure gravity [6][7][8][9][10][11][12][13][14] as well as with matter [15][16][17][18][19] has been discovered, for reviews see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32]. This fixed point provides a UV completion for a quantum field theory of the…”

Section: Jhep01(2018)030mentioning

confidence: 99%

Upper bound on the Abelian gauge coupling from asymptotic safety

Eichhorn

Versteegen

2018

J. High Energ. Phys.

121

167

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Abstract:We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35 % above the infrared value of the hypercharge coupling in the Standard Model.

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“…(4) via an RG improvement is the identification of the cutoff scale k with a suitable physical quantity. Such a procedure allows one to analyze the effects of quantum gravity in a variety of single-scale settings [31]. Since we have seen that, generically, any quantum-gravity modification of the form ∇ 2 x → ∆ will result in functions P (x, x ′ , σ) that have no interpretation as probability densities, we will explore an alternative RG-improvement scheme where the scale k is related to the diffusion time σ.…”

Section: A Diffusion In Nonlinear Timementioning

confidence: 99%

“…This, for instance, was the proposal for multifractional Brownian motion [33,[54][55][56] or other multiscale processes [43]. For the remainder of this section we will focus on the multiscale geometries emerging within asymptotically safe gravity, [9,10,31].…”

Section: Multiscale Diffusion Processesmentioning

confidence: 99%

Probing the quantum nature of spacetime by diffusion

2013

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Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semidefinite probability densities, applicable to asymptotically safe gravity, Hořava-Lifshitz gravity and loop quantum gravity. These recover all previous results on the spectral dimension and shed further light on the structure of the quantum spacetimes by assessing the underlying stochastic processes. Pointing out that manifestly different diffusion processes lead to the same spectral dimension, we propose the probability distribution of the diffusion process as a refined probe of quantum spacetime.

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Asymptotic Safety, Fractals, and Cosmology

Cited by 61 publications

References 159 publications

Diffusion in multiscale spacetimes

Diffusion in multiscale spacetimes

Upper bound on the Abelian gauge coupling from asymptotic safety

Probing the quantum nature of spacetime by diffusion

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