Spectral dimension of the universe in quantum gravity at a lifshitz point.

By Petr Hořava. Physical Review Letters, 2009

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We extend the definition of "spectral dimension" d_{s} (usually defined for fractal and lattice geometries) to theories in spacetimes with anisotropic scaling. We show that in gravity with dynamical critical exponent z in D+1 dimensions, the spectral dimension of spacetime is d_{s}=1+D/z. In the case of gravity in 3+1 dimensions with z=3 in the UV which flows to z=1 in the IR, the spectral dimension changes from d_{s}=4 at large scales to d_{s}=2 at short distances. Remarkably, this is the behavior found numerically by Ambjørn et al. in their causal dynamical triangulations approach to quantum gravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/36b9806fcedeefac49bc46d6e414b3d54b068f20

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Citations in the corpus

The renormalizability of Hořava–Lifshitz-type gravities (2009, background): “uments. Horava–Lifshitzˇ (HL) gravity has sparked a lot of interest. A number of follow–up works have been published concerning its solutions (see e.g. [3, 4]) and cosmological implications (see e.g. [5, 6, 7, 8, 9, 10]), but many fundamental questions have not yet been answered. In this present not”
On the z=4 Horava-Lifshitz Gravity (2009, neutral): “1Email: cairg@itp.ac.cn 2Email: liuyan@itp.ac.cn 3Email: sunyw@itp.ac.cn”
Quantum-Spacetime Phenomenology (2008, result): “Two spectral dimensions for small diffusion times was then also found in studies inspired by asymptotic safety [360, 467] and studies based on Hořava–Liftschitz gravity [290].”
Dimension and dimensional reduction in quantum gravity (2017, background): “to quantum gravity is to modify the Lagrangian to make the theory renormalizable. In one such approach, Hoˇrava-Lifshitz gravity [52], a generalized spectral dimension, ﬂows to d = 2 at high energies [53], as do the thermodynamic dimensions [54]. In curvature-squared models, the Greens function dime”
hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System (2016, background): “The models can be extended even further to those which contain higher derivatives in space but not in time [44–47].”
Horava-Lifshitz Cosmology (2009, background): “Further properties include a UV spectral dimension that is two [7], as well the appearance of”
Modified Gravity and Cosmology (2011, background): “Hořava-Lifschitz (HL) gravity was proposed as a toy model of quantum gravity [618, 619, 620].”
Field theory at a Lifshitz point (2009, background): “In addition, we also discuss the thermal dynamics and the size of causal patch in a FRW universe for the field theory at a Lifshitz point.”
Strong coupling in Horava gravity (2009, background): “Hořava has recently proposed an interesting toy model of quantum gravity [1–3], generating a whole slew of publications that examine various aspects of the theory (see, for example [4–9]).”
Nonperturbative quantum gravity (2012, background): “This anomalous scaling near the fixed point is the reason why the spectral dimension in both the asymptotic safety and the Hořava-Lifshiz scenario is 2 and not 4 [97, 111].”
Quantum gravity without Lorentz invariance (2009, background): “Hořava’s “Lifschitz point gravity” [1–3], a field theoretic quantum gravity model based on “anisotropic scaling” of the space and time dimensions, has recently attracted a tremendous amount of attention.”
Born–Infeld inspired modifications of gravity (2017, background): “The same authors pursued a similar approach in [186] to construct theories that recover Horava’s gravity [210, 211] in 3 dimensions at quadratic order.”
Matter bounce in Horava-Lifshitz cosmology (2009, background): “Recently, Hořava (based on the pioneering work of [1] has proposed [2, 3] a model for quantum gravity which is power-counting renormalizable and hence potentially ultra-violet (UV) complete.”