Multidimensional Gravity Research Articles

Complex Network Construction and Pattern Recognition of China’s Provincial Low-Carbon Economic Development with Long Time Series: Based on the Detailed Spatial Relationship

Low-carbon economic development has become the orientation of high-quality economic construction in the era of climate change. Because it involves multi-dimensional elements and is driven by the concept of regional integration and common development, the development pattern among China’s provinces should show the characteristics of complex networked spatial correlation. However, most of the existing research are for is based on attribute data and combined with traditional spatial econometric models, which cannot describe the complex networked spatial correlation. Concurrently, the network construction is mainly based on undirected-unweighted sparseness, which makes it difficult to truly restore the asymmetric detailed spatial relationship, making the related research about development pattern recognition and its evolution based on the detailed spatial relationship relatively lacking. Therefore, based on the perspective of relational data, this study constructs a multi-dimensional gravity model by using the comprehensive quality of China’s provincial low-carbon economic development, measured by the multi-dimensional evaluation index system and dynamic weight method, and the comprehensive distance based on geography, society, economy, and adjacency. And then the spatial correlation strength among China’s provincial low-carbon economic development is determined, and constructs a directed-weighted complex network. Then, it further explores the inter-provincial detailed spatial relationship of low-carbon economy development from the three dimensions of overall, individual and group, to recognize the development patterns and evolution rules of low-carbon economic development in different provinces, and clarify the development orientation. The results show that, during the study period, the spatial correlation of China’s provincial low-carbon economic development has become increasingly close, showing a complex networked correlation structure with multi-linearity, asymmetry, and geographical proximity as a whole. The division of general structure is consistent with China’s regional economic development strategy. The unbalanced development of China’s provincial low-carbon economy is the result of multi-center drive in the eastern and central regions, and the distance from the network center in the western regions. In general, China’s provincial low-carbon economic development patterns can be roughly divided into spillover, main bridge, auxiliary bridge, and benefit type. In the future, we should make full use of the power source role of spillover provinces, and the bridge support role of bridge provinces to drive the development of benefit provinces. Among them, Chongqing, Shaanxi, Hebei and Sichuan are expected to become new regional growth poles. The research on the inter-provincial spatial correlation effect and development pattern recognition of low-carbon economic development is expected to provide guidance for the sustainable development of low-carbon economy in China.

Program of Searches with the CMS Detector for Signals from Multidimensional Low-Energy Gravity at the Large Hadron Collider

This article, presented on behalf of the Compact Muon Solenoid (CMS) Collaboration, gives a generalizing survey of the results of the CMS experiment that concern searches for Kaluza–Klein excited states of the graviton (KK modes) and for microscopic multidimensional black holes, quantum black holes, and string balls within multidimensional low-energy gravity. The present analysis relies on data obtained during the first (2010–2012) and second (2015–2018) stages of operation of the Large Hadron Collider (LHC) in proton–proton collisions at the center-of-mass energies of 7, 8, and 13 TeV. The results of experimental searches are interpreted in terms of constraints on the space of parameters of the theoretical models being studied. Also, further prospects for the HL-LHC mode and for the possible Future Circular Collider (FCC) are discussed briefly.

Multidimensional gravity with higher derivatives and inflation

We elaborate on the inflationary model starting from multidimensional Lagrangian and gravity with second-order curvature terms. The effective scalar field is related to the Ricci scalar of extra dimensions. It is shown that the Kretschmann and the Ricci tensor square terms dominate during inflation. The observable values of the spectral index and the tensor-to-scalar ratio are obtained for specific values of the model parameters.

On Cosmology in Nonlinear Multidimensional Gravity with Multiple Factor Spaces

Within the scope of multidimensional Kaluza--Klein gravity with nonlinear curvature terms and two spherical extra spaces of dimensions $m$ and $n$, we study the properties of an effective action for the scale factors of the extra dimensions. Dimensional reduction leads to an effective 4D multiscalar-tensor theory. Based on qualitative estimates of the Casimir energy contribution on a physically reasonable length scale, we demonstrate the existence of such sets of initial parameters of the theory in the case $m=n$ that provide a minimum of the effective potential that yield a fine-tuned value of the effective 4D cosmological constant. The corresponding size of extra dimensions depends of which conformal frame is interpreted as the observational one: it is about three orders of magnitude larger than the standard Planck length if we adhere to the Einstein frame, but it is $n$-dependent in the Jordan frame, and its invisibility requirement restricts the total dimension to values $D = 4+2n \leq 20$.

On generalized Melvin’s solutions for Lie algebras of rank 2

We consider a class of solutions in multidimensional gravity which generalize Melvin’s well-known cylindrically symmetric solution, originally describing the gravitational field of a magnetic flux tube. The solutions considered contain the metric, two Abelian 2-forms and two scalar fields, and are governed by two moduli functions H1(z) and H2(z) (z = ρ2, ρ is a radial coordinate) which have a polynomial structure and obey two differential (Toda-like) master equations with certain boundary conditions. These equations are governed by a certain matrix A which is a Cartan matrix for some Lie algebra. The models for rank-2 Lie algebras A2, C2 and G2 are considered. We study a number of physical and geometric properties of these models. In particular, duality identities are proved, which reveal a certain behavior of the solutions under the transformation ρ → 1/ρ; asymptotic relations for the solutions at large distances are obtained; 2-form flux integrals over 2-dimensional regions and the corresponding Wilson loop factors are calculated, and their convergence is demonstrated. These properties make the solutions potentially applicable in the context of some dual holographic models. The duality identities can also be understood in terms of the Z2 symmetry on vertices of the Dynkin diagram for the corresponding Lie algebra.

Exact solutions and critical chaos in dilaton gravity with a boundary

We consider (1 + 1)-dimensional dilaton gravity with a reflecting dynamical boundary. The boundary cuts off the region of strong coupling and makes our model causally similar to the spherically-symmetric sector of multidimensional gravity. We demonstrate that this model is exactly solvable at the classical level and possesses an on-shell SL(2, ℝ) symmetry. After introducing general classical solution of the model, we study a large subset of soliton solutions. The latter describe reflection of matter waves off the boundary at low energies and formation of black holes at energies above critical. They can be related to the eigenstates of the auxiliary integrable system, the Gaudin spin chain. We argue that despite being exactly solvable, the model in the critical regime, i.e. at the verge of black hole formation, displays dynamical instabilities specific to chaotic systems. We believe that this model will be useful for studying black holes and gravitational scattering.

Cosmology in nonlinear multidimensional gravity and the Casimir effect

We study the possible cosmological models in Kaluza-Klein-type multidimensional gravity with a curvature-nonlinear Lagrangian and a spherical extra space, taking into account the Casimir energy. First, we find a minimum of the effective potential of extra dimensions, leading to a physically reasonable value of the effective cosmological constant in our 4D space-time. In this model, the huge Casimir energy density is compensated by a fine-tuned contribution of the curvature-nonlinear terms in the original action. Second, we present a viable model with slowly evolving extra dimensions and power-law inflation in our space-time. In both models, the results formulated in Einstein and Jordan frames are compared.

On nonlinear multidimensional gravity and the Casimir effect

We study the possible cosmological models in Kaluza-Klein-type multidimensional gravity with a curvature-nonlinear Lagrangian and a spherical extra space, taking into account the Casimir energy. First, we find a minimum of the effective potential of extra dimensions, leading to a physically reasonable value of the effective cosmological constant in our 4D space-time. In this model, the huge Casimir energy density is compensated by a fine-tuned contribution of the curvature-nonlinear terms in the original action. Second, we present a viable model with slowly evolving extra dimensions and power-law inflation in our space-time. In both models, the results formulated in Einstein and Jordan frames are compared.

Integrable multidimensional gravitational and cosmological models and applications

Two families of exact solutions in multidimensional gravity with scalar fields and fields of forms are considered: fluxbrane and black brane ones. A brief overview of main results on billiard approach for cosmological-type models with branes is also presented.

Hierarchi problem

The way to solve the hierarchy problem based on multidimensional gravity is discussed. Various metrics of deformed extra space are produced at the Planck scale. It is shown that the Higgs vacuum value depends on a metric of extra space and hence their different numerical values are realized in various universes. An interval of the Higgs vacuum values is proved include zero value. Our universe belongs to a set of universes the vacuum values of which are close to zero

Deformed compact extra space as dark matter candidate

We elaborate the possibility for a deformed extra space to be considered as the dark matter candidate. To perform calculations, a class of two-dimensional extra metrics was considered in the framework of the multidimensional gravity. It was shown that there exists a family of stationary metrics of the extra space possessing point-like defect. Estimation of cross-section of scattering of a particle of the ordinary matter on a spatial domain with deformed extra space is in agreement with the observational constraints.

Searches for Kaluza-Klein graviton excitations and microscopic black holes with the aid of the CMS detector at the LHC

A survey of the results of the Compact Muon Solenoid (CMS) experiment that concern searches for massive Kaluza-Klein graviton excitations and microscopic black holes, quantum black holes, and string balls within models of low-energy multidimensional gravity is presented on behalf of the CMS Collaboration. The analysis in question is performed on the basis of a complete sample of data accumulated for proton-proton collisions at the c.m. energies of 7 and 8 TeV at the Large Hadron Collider (LHC) over the period spanning 2010 and 2012.

The role of initial conditions in the universe formation

The dependence of low-energy physics on initial conditions in the framework of multidimensional gravity is discussed. It is shown that the observable symmetries could be a result of specific topologies originating from space-time foam.

Multidimensional gravity, flux and black brane solutions governed by polynomials

Two families of composite black brane solutions are overviewed, fluxbrane and black brane ones, in a model with scalar fields and fields of forms. The metric of any solution is defined on a manifold which contains a product of several Ricci-flat “internal” spaces. The solutions are governed by moduli functions $\mathcal{H}_s $ (for fluxbranes) and H s (for black branes), obeying nonlinear differential equations with certain boundary conditions. Themaster equations for $\mathcal{H}_s $ and H s are equivalent to Toda-like equations and depend on a nondegenerate matrix A related to brane intersection rules. The functions H s and $\mathcal{H}_s $ , as was conjectured and confirmed (at least partly) earlier, should be polynomials in proper variables if A is a Cartan matrix of some semisimple finite-dimensional Lie algebra. The fluxbrane polynomials $\mathcal{H}_s $ were shown to be used for the construction of black brane polynomials H s . This approach is illustrated by examples of nonextremal electric black p-brane solutions related to Lie algebras A 2, C 2, and G 2.

Nonlinear multidimensional gravity and the Australian dipole

The existing observational data on possible variations of fundamental physical constants (FPC) confirm more or less confidently only a variability of the fine structure constant $\alpha$ in space and time. A model construction method is described, where variations of $\alpha$ and other FPCs (including the gravitational constant $G$) follow from the dynamics of extra space-time dimensions in the framework of curvature-nonlinear multidimensional theories of gravity. An advantage of this method is a unified approach to variations of different FPCs. A particular model explaining the observable variations of $\alpha$ in space and time has been constructed. It comprises a FRW cosmology with accelerated expansion, perturbed due to slightly inhomogeneous initial data.

Searches for signals from microscopic black holes in processes of proton collisions at $\sqrt s $ = 7 TeV in the CMS experiment at the LHC

If the fundamental scale of multidimensional gravity is about one or several TeV units, microscopic black holes or objects referred to as string balls may be produced at the LHC. The most recent results obtained by the CMS Collaboration at the LHC from searches for such signals at the c.m. protoninteraction energy of 7 TeV and for an integrated luminosity of 4.7 fb−1. Lower limits on the masses of objects of strongly acting gravity were set in the parameter region accessible to tests at the present time. Prospects for further research in this field are discussed.

Variations of α and G from nonlinear multidimensional gravity

To explain the recently reported large-scale spatial variations of the fine structure constant $\alpha$, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities as compared with the Planck scale, the original theory reduces to a multi-scalar field theory in four dimensions. On this basis, we consider different variants of isotropic cosmological models in both Einstein and Jordan conformal frames. One of the models turns out to be equally viable in both frames, but in the Jordan frame the model predicts simultaneous variations of $\alpha$ and the gravitational constant $G$, equal in magnitude. Large-scale small inhomogeneous perturbations of these models allow for explaining the observed spatial distribution of $\alpha$ values.

Low energy physics and properties of extra space

The mechanism of low energy physics formation in the framework of multidimensional gravity is discussed. It is shown that a wide set of parameters of a primary theory could lead to the observable Universe. Quantum fluctuations of extra space metric and its consequent classical evolution play an important role in this process.

Emergence of symmetries

The mechanism of symmetry formation is discussed in the framework of multidimensional gravity. It is shown that this process is strictly connected to the entropy decrease of compact space. The existence of low energy symmetries is not postulated from the beginning. They could be absent during the inflationary stage under certain conditions discussed in the Letter.

Gauss-bonnet black holes and possibilities for their experimental search

Corollaries of gravity models with second-order curvature corrections in the form of a Gauss-Bonnet term and possibilities (or impossibilities) for their experimental search or observations are discussed. The full version of the four-dimensional Schwarzschild-Gauss-Bonnet black hole solution and the constraint on the possible minimal black hole mass following from this model are considered. Using our solution as a model for the final stages of Hawking evaporation of black holes with a low initial mass (up to 1015 g) whose lifetime is comparable to that of our Universe, we have revealed differences in the patterns of evaporation: we have obtained high values of the emitted energy and showed the impossibility of an experimental search for primordial black holes by their evaporation products. Scenarios for the evaporation of Gauss-Bonnet black holes in multidimensional gravity models and possibilities for their experimental search are also discussed.