The spectral dimension of the universe is scale dependent

We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four dimensional on large scales, the quantum universe appears two dimensional at short distances. We conclude that quantum gravity may be "self-renormalizing" at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction.     

Random versus holographic fluctuations of the background metric. I. (Cosmological) running of space–time dimension

A profound quantum-gravitational effect of space–time dimension running with respect to the size of space–time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this Letter is twofold. First, we find that box-counting dimension in face of finite resolution of space–time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newton's inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections.     

Evidence for asymptotic safety from lattice quantum gravity

We calculate the spectral dimension for nonperturbative quantum gravity defined via Euclidean dynamical triangulations. We find that it runs from a value of ～3/2 at short distance to ～4 at large distance scales, similar to results from causal dynamical triangulations. We argue that the short-distance value of 3/2 for the spectral dimension may resolve the tension between asymptotic safety and the holographic principle.     

Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations

We explore the ultraviolet continuum regime of causal dynamical triangulations, as probed by the flow of the spectral dimension. We set up a framework in which one can find continuum theories that can in principle fully reproduce the behavior of the latter in this regime. In particular, we show that, in 2 + 1 dimensions, Ho?ava-Lifshitz gravity can mimic the flow of the spectral dimension in causal dynamical triangulations to high accuracy and over a wide range of scales. This seems to provide evidence for an important connection between the two theories.     

Some Properties of Multigravity Theories and Discretized Brane Worlds

We review some properties of solutions to 5D Einstein gravity with a discrete fifth dimension. Those properties depend on the discretization scheme we use. In particular, we find that the neglect of the lapse field (along the discretized direction) gives rise to Randall–Sundrum-type metric with a negative tension brane. However, no brane source is required. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We show also that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales.     

Properties of Gravitational Waves in Cosmological General Relativity

The 5D Cosmological General Relativity theory developed by Carmeli reproduces all of the results that have been successfully tested for Einstein's 4D theory. However the Carmeli theory because of its fifth dimension, the velocity of the expanding universe, predicts something different for the propagation of gravity waves on cosmological distance scales. This analysis indicates that gravitational radiation may not propagate as an unattenuated wave where effects of the Hubble expansion are felt. In such cases the energy does not travel over very large length scales but is evanescent and dissipated into the surrounding space as heat.     

New experimental constraints on non-Newtonian forces below 100 microm

We have searched for large deviations from Newtonian gravity by means of a finite-frequency microcantilever-based experiment. Our data eliminate from consideration mechanisms of deviation that posit strengths approximately 10(4) times Newtonian gravity at length scales of 20 microm. This measurement is 3 orders of magnitude more sensitive than others that provide constraints at similar length scales.     

Large-scale–small-scale duality and the cosmological constant

We study a model of quantum cosmology originating from a classical model of gravitation where a self-interacting scalar field is coupled to gravity with the metric undergoing a signature transition. We show that there are dual classical signature changing solutions, one at large scales and the other at small scales. It is possible to fine-tune the physics in both scales with an infinitesimal effective cosmological constant.     

Nonquantum Gravity

One of the great challenges for 21st century physics is to quantize gravity and generate a theory that will unify gravity with the other three fundamental forces of nature. This paper takes the (heretical) point of view that gravity may be an inherently classical, i.e., nonquantum, phenomenon and investigates the experimental consequences of such a conjecture. At present there is no experimental evidence of the quantum nature of gravity and the likelihood of definitive tests in the future is not at all certain. If gravity is, indeed, a nonquantum phenomenon, then it is suggested that evidence will most likely appear at mesoscopic scales.     

KPZ in One Dimensional Random Geometry of Multiplicative Cascades

We prove a formula relating the Hausdorff dimension of a subset of the unit interval and the Hausdorff dimension of the same set with respect to a random path matric on the interval, which is generated using a multiplicative cascade. When the random variables generating the cascade are exponentials of Gaussians, the well known KPZ formula of Knizhnik, Polyakov and Zamolodchikov from quantum gravity [KPZ88] appears. This note was inspired by the recent work of Duplantier and Sheffield [DS08] proving a somewhat different version of the KPZ formula for Liouville gravity. In contrast with the Liouville gravity setting, the one dimensional multiplicative cascade framework facilitates the determination of the Hausdorff dimension, rather than some expected box count dimension.     

The dark-baryonic matter mass relation for observational verification in Verlinde’s emergent gravity

Recently, a new interesting idea of origin of gravity has been developed by Verlinde. In this scheme of emergent gravity, where horizon entropy, microscopic de Sitter states and relevant contribution to gravity are involved, an entropy displacement resulting from matter behaves as a memory effect and can be exhibited at sub-Hubble scales, namely, the entropy displacement and its “elastic” response would lead to emergent gravity, which gives rise to an extra gravitational force. Then galactic dark matter effects may origin from such extra emergent gravity. We discuss some concepts in Verlinde’s theory of emergent gravity and point out some possible problems or issues, e.g., the gravitational potential caused by Verlinde’s emergent apparent dark matter may no longer be continuous in spatial distribution at ordinary matter boundary (such as a massive sphere surface). In order to avoid the unnatural discontinuity of the extra emergent gravity of Verlinde’s apparent dark matter, we suggest a modified dark-baryonic mass relation (a formula relating Verlinde’s apparent dark matter mass to ordinary baryonic matter mass) within this framework of emergent gravity. The modified mass relation is consistent with Verlinde’s result at relatively small scales (e.g., \(R<3h_{70}^{-1}\) Mpc). However, it seems that, compared with Verlinde’s relation, at large scales (e.g., gravitating systems with \(R>3h_{70}^{-1}\) Mpc), the modified dark-baryonic mass relation presented here might be in better agreement with the experimental curves of weak lensing analysis in the recent work of Brouwer et al. Galactic rotation curves are compared between Verlinde’s emergent gravity and McGaugh’s recent model of MOND (Modified Newtonian Dynamics established based on recent galaxy observations). It can be found that Verlinde rotational curves deviate far from those of McGaugh MOND model when the MOND effect (or emergent dark matter) dominates. Some applications of the modified dark-baryonic mass relation inspired by Verlinde’s emergent gravity will be addressed for galactic and solar scales. Potential possibilities to test this dark-baryonic mass relation as well as apparent dark matter effects, e.g., planetary perihelion precession at Solar System scale, will be considered. This may enable to place some constraints on the magnitudes of the MOND characteristic acceleration at the small solar scale.     

Kaluza-Klein space and strong gravity

A study of strong gravity theory is carried out in five-dimensional Kaluza-Klein space-time. A relation between the cosmological constant and the radius parameter of the fifth dimension is obtained. The effect of the extra dimension is seen through the generation of masses simulating a Regge-like mass spectrum. It is found that the confinement mechanism is built into the strong gravity formalism. We also discuss the trapping of quarks in the 5D background.     

Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at “quantum scales” and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a “semiclassical” state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity.     

Resolving Curvature Singularities in Holomorphic Gravity

We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature singularity. Likewise, typical observers do not experience Big Bang singularity. Unlike Hermitian gravity (Mantz and Prokopec in , 2008), holomorphic gravity does not respect the reciprocity symmetry and thus it is mainly a toy model for a gravity theory formulated on complex space-times. Yet it is a model that deserves a closer investigation since in many aspects it resembles Hermitian gravity and yet calculations are simpler. Our study of light bending and gravitational waves in weak holomorphic gravitational fields strongly suggests that holomorphic gravity reduces to general relativity at large distance scales.     

Gravity-free hydraulic jumps and metal femtoliter cups

Hydraulic jumps created by gravity are seen everyday in the kitchen sink. We show that at small scales a circular hydraulic jump can be created in the absence of gravity by surface tension. The theory is motivated by our experimental finding of a height discontinuity in spreading submicron molten metal droplets created by pulsed-laser ablation. By careful control of initial conditions, this leads to solid femtoliter cups of gold, silver, copper, niobium, and tin.     

Primordial gravity waves and weak lensing

Inflation produces a primordial spectrum of gravity waves in addition to the density perturbations which seed structure formation. We compute the signature of these gravity waves in the large scale shear field. The shear can be divided into a gradient mode (G or E) and a curl mode (C or B). The latter is produced only by gravity waves, so the observations of a nonzero curl mode could be seen as evidence for inflation. We find that the expected signal from inflation is small, peaking on the largest scales at l(l+1)C(l)/2pi<10(-11) at l=2 and falling rapidly thereafter. Even for an all-sky deep survey, this signal would be below noise at all multipoles.     

Galilean-invariant scalar fields can strengthen gravitational lensing

The mystery of dark energy suggests that there is new gravitational physics on long length scales. Yet light degrees of freedom in gravity are strictly limited by Solar System observations. We can resolve this apparent contradiction by adding a Galilean-invariant scalar field to gravity. Called Galileons, these scalars have strong self-interactions near overdensities, like the Solar System, that suppress their dynamical effect. These nonlinearities are weak on cosmological scales, permitting new physics to operate. In this Letter, we point out that a massive-gravity-inspired coupling of Galileons to stress energy can enhance gravitational lensing. Because the enhancement appears at a fixed scaled location for dark matter halos of a wide range of masses, stacked cluster analysis of weak lensing data should be able to detect or constrain this effect.     

热中子星r-mode 不稳定性的研究

理论上,不稳定的中子星r-mode 能辐射可探测的引力波。采用具有超软对称能的非对称核物质物态方程,并考虑非牛顿引力效应影响,数值计算了由于CFS(Chandrasekhar-Friedmann-Schutz) 不稳定性引起的年轻热中子星的r-mode 不稳定窗口,给出了引力辐射时标和耗散时标随温度的变化关系。利用中子星观测对非牛顿引力参数的约束,给出了热中子星在高温区不稳定窗口边界的约束,并发现较大的非牛顿引力参数对应着较宽的r-mode 不稳定窗口。研究结果可为地面引力辐射探测提供有意义的参考。Theoritically, instable r-mode in neutron star may radiate detectable gravitational waves. In this work,considering the non-Newtonian gravity proposed in the grand unification theories, we numerically calculate the CFS instabilities of r-mode s in the hot neutron stars by using an equation of state with super-soft symmetry energies. The changes of the gravitational radiation time scales and the viscous time scales versus the stellar temperatures are obtained.And according to the constraint of the neutron star observation on the parameter of non-Newtonian gravity, the constraint on the boundary of the instability window is also given. It is found that a stronger non-Newtonian gravity corresponds with a wider r-mode instability window. These results may provide interesting reference for the gravitational wave detection.     

Model for gravity at large distances

We construct an effective model for gravity of a central object at large scales. To leading order in the large radius expansion we find a cosmological constant, a Rindler acceleration, a term that sets the physical scales, and subleading terms. All these terms are expected from general relativity, except for the Rindler term. The latter leads to an anomalous acceleration in geodesics of test particles.