Spatial Curvature Research Articles

Color-kinematics duality for nonlinear sigma models with nonsymmetric cosets

We propose an extension of the color-kinematics duality for nonlinear sigma models with nonymmetric cosets. The role of color is replaced with curvatures in field space. The duality between curvature and kinematics allows for a new double copy: the double copy of the nonlinear sigma model for nonsymmetric cosets is the general Galileon theory. We provide evidence for this new double copy of geometry. Published by the American Physical Society 2024

Spooky Black Holes and Gravitomagnetism

Wide spread misconceptions about the reality of space curvature in General Relativity (GR) and their relevance in connection to the existence of black holes are revisited. The mean life of proposed black holes is estimated and their practical non existence is emphasized. The repulsive effect of gravitational self energy is underlined. The relevance of gravitomagnetism to account for alleged black hole effects is stressed.

Atomic disorder and intrinsic anomalous Hall effect in a half-metallic ferromagnet Co2VAl

Half-metallic ferromagnets, conducting for one spin channel while insulating for the other, are highly desirable for spintronic applications due to 100 % spin polarization around the Fermi level. Cobalt-based half-metallic Heusler compounds have attracted enormous attention due to their large spin polarization and a high magnetic transition temperature. In the present study, we report the experimental and theoretical investigation of crystal structure and anomalous Hall effect (AHE) in half-metallic ferromagnet Co2VAl. The structural investigation of high-resolution synchrotron x-ray diffraction data reveals 10 % antisite disorder between V and Al atoms within the L21 ordered crystal structure. The scaling analysis of anomalous Hall data shows that the AHE in our system is mainly driven by the Berry curvature in the momentum space. The magnitude of experimental intrinsic anomalous Hall conductivity (AHC) due to the momentum space Berry curvature is about 44.67 ± 0.02 S/cm at 5 K, which is less than the theoretically calculated AHC for the ordered structure. Our theoretical calculations suggest that the lower AHC obtained for the present system is due to the reduced Berry curvature in the disordered case with negligible impact on half-metallicity of the system.

Gravastars formation with back-reaction effects from extended general relativity

Using an extended theory of General Relativity that incorporates normalized relativistic velocities, where the boundary terms in the varied Einstein–Hilbert action are considered. Within this context, I investigate the dynamic evolution of a collapsing spherical system characterized by a metric with spatial curvature and variable time-scale, aiming to describe the process of Gravastar formation. To illustrate the system’s dynamics, I analyze a power-law collapsing scenario and derive the equation of state for both cases, with and without geometrical perturbations. In particular, I derive the equation of state, incorporating back-reaction effects related with the boundary terms of the varied Einstein–Hilbert action.

Classical mechanics in noncommutative spaces: confinement and more

We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the corresponding phase space is given by the cotangent bundle of a Lie group, with the Lie group playing the role of a curved momentum space. We show that the curvature of the momentum space may lead to rather unexpected physical phenomena such as an upper bound on the velocity of a free nonrelativistic particle, bounded motion for repulsive central force, and no-fall-into-the-centre for attractive Coulomb potential. We also consider a superintegrable Hamiltonian for the Kepler problem in 3-space with su(2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {su}(2)$$\\end{document} noncommutativity. The leading correction to the equations of motion due to noncommutativity is shown to be described by an effective monopole potential.

A natural model for curved inflation

Abstract Inflationary models with a non-zero background curvature require additional hy- pothesis or parameters compared to flat inflation and the procedure to construct them cannot be as simple as in the flat case. For this reason, there is no consen- sus on the primordial power spectrum that should be considered at large scales in a curved Universe. In this letter, we propose a model of curved inflation in which the usual canonical quantization and Bunch–Davies vacuum choice of the flat case can be considered. The framework is a recently proposed modification of general relativity in which a non-dynamical topological term is added to the Einstein equation. The model is universal as it is the same for any background curvature, and no additional parameters or hypothesis on the initial spatial curvature are introduced. This gives a natural and simple solution to the problem of constructing curved inflation, and at the same time provides an additional argument for this topological modification of general relativity.

Revisiting the effect of lens mass models in cosmological applications of strong gravitational lensing

Abstract Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al. (2019) in order to constrain both lens and cosmological parameters for: (i) the standard ΛCDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, ΩM0 → 0. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to fv0 → 0.73 and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values fv0 ∈ {0.1, 0.9}, and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger datasets soon available, separation of cosmology and lens models must be addressed.

Lorentz attractor excitation-based structural damage identification using state space curvature reconstruction- enhanced transformer

Abstract Vibration-based structural damage identification has been widely investigated. Different from previous studies that analyze vibrational responses in time and frequency domains, a new Lorentz attractor excitation-based damage identification is becoming a novel strategy with the advantage of capturing the structure’s nonlinear dynamic effects. In this study, Lorentz attractor-based chaotic signals were employed as excitation signals for the structural damage identification of a frame structure. Nonlinear responses were recorded and damages of bolt looseness at different locations were considered. The structural damages could be revealed in the state-space plot of the responses. A state space curvature reconstruction method was introduced to enhance the key features of the nonlinear responses. A small-sample damage identification is performed using a deep learning algorithm – a Transformer with an accuracy of 92.38%. The advantages of the proposed method over conventional deep learning algorithms were validated. The proposed method can be applied to health conditions identification of buildings, bridges, and trusses.

Vacuum currents in curved tubes

We investigate the combined effects of spatial curvature and topology on the properties of the vacuum state for a charged scalar field localized on rotationally symmetric 2D curved tubes. For a general spatial geometry and for quasiperiodicity condition with a general phase, the representation of the Hadamard function is provided where the topological contribution is explicitly extracted. As an important local characteristic of the vacuum state the expectation value of the current density is studied. The vacuum current is a periodic function of the magnetic flux enclosed by the tube with the period of flux quantum. The general formula is specified for constant radius and conical tubes. As another application, we consider the Hadamard function and the vacuum current density for a scalar field on the Beltrami pseudosphere. Several representations are provided for the corresponding expectation value. For small values of the proper radius of the tube, compared with the curvature radius, the effect of spatial curvature on the vacuum current is weak and the leading term in the corresponding expansion coincides with the current density on a constant radius tube. The effect of curvature is essential for proper radii of the tube larger than the radius of spatial curvature. In this limit the falloff of the current density, as a function of the proper radius, follows a power law for both massless and massive fields. This behavior is in clear contrast to the one for a constant radius tube with exponential decay for massive fields. We also compare the vacuum currents on the Beltrami pseudosphere and on locally de Sitter and anti–de Sitter 2D tubes. Published by the American Physical Society 2024

An Experiment to Test a New Theory in Physics, Fundamentally Different From General Relativity, by Changing the Speed of Light in Electromagnetic Interaction

The fundamental foundation for Einstein’s Theory of General Relativity is the “Curvature of Space and Time” due to a Gravitational Field. In the “Theory o f General Relativity” Gravitational RedShift has been explained by a change in time and space resulting is a change in the observed frequency shift in the spectrum o f the light being emitted by far away Galaxies. The foundation for Einstein’s theory o f General Relativity is a constant value for the speed o f light in the absence of a gravitational field. In the “New Theory” the fundamental foundation is “Equilibrium”. Equilibrium for the “5 fundamental force densities in light” in any direction at any time and at any location. The New Theory describes a changing in the speed of light when corresponding monochromatic beams of light (highly coherent LASER beams) cross each other in different directions which effect would be in contradiction with the fundamental assumption in General Relativity of a constant speed of light. This experiment will be a deter mining test for the New Theory in Physics.

Peculiar velocities in Friedmann universes with nonzero spatial curvature

We extend the earlier linear studies of cosmological peculiar velocities to Friedmann universes with nonzero spatial curvature. In the process, we also compare our results with those obtained in cosmologies with Euclidean spatial sections. Employing relativistic cosmological perturbation theory, we first provide the differential formulas governing the evolution of peculiar velocities on all Friedmann backgrounds. The technical complexities of the curved models, however, mean that analytic solutions are possible only in special, though characteristic, moments in the lifetime of these universes. Nevertheless, our solutions exhibit persistent patterns that make us confident enough to generalize them. Thus, we confirm earlier claims that, compared to the Newtonian and the quasi-Newtonian studies, the relativistic analysis supports considerably stronger linear growth rates for peculiar-velocity perturbations. This result holds irrespective of the background curvature. Moreover, for positive curvature, the peculiar growth rate is found to be faster than that obtained in a spatially flat Friedman universe. In contrast, linear peculiar velocities appear to grow at a slower pace when their Friedmann host is spatially open. Extrapolating them to the present, our results seem to suggest faster bulk peculiar motions in overdense, rather than in underdense, regions of the Universe. Published by the American Physical Society 2024

Dynamics of cosmic string formation with emission of gravitational waves: a toy model

Starting from an extended theory of general relativity with boundary terms included, we study a toy model to describe the dynamical collapse of an infinite cylinder with positive spatial curvature from which a cosmic string is formed after collapsing, and we examine the production of gravitational waves (GW) emitted during the collapse. The background dynamics of the radial collapse is described by a massive scalar field which departs from the equilibrium when the scalar field climbs through the quadratic potential. During the collapse the radial pressure is considered as null, so that the kinetic and the potential energy densities are equaled. The components of the GW modes +,×and B, for the polarization tensor, are analytically obtained.

A Study of Time Evolution of Some Cosmological Parameters in The Framework of an Anisotropic Kaluza-Klein Metric Using an Empirical Exponential Scale Factor

The present study attempts to determine the time dependence of some cosmological parameters in flat space (i.e., a space of zero spatial curvature), in the framework of an anisotropic Kaluza-Klein metric. The field equations for this work have been derived from the metric by assuming a power-law relation between the normal scale factor and the scale factor corresponding to the extra (i.e., the fifth) dimension. An empirical scale factor, having the expression of a = B exp(αtβ), has been used here in order to derive the expressions for some cosmological parameters as functions of time. The reason for choosing this scale factor is that it generates an expression for the deceleration parameter which undergoes a change of sign, as time goes on, from positive to negative, indicating a transition of the universe from an initial state of decelerated expansion to that of an accelerated expansion (which is its present state), as has been inferred from astrophysical observations. We have graphically depicted the evolution of some cosmological parameters with respect to what one may call the relative time, expressed as t/t0, where t0 is the present age of the universe. The present study finds the dynamical cosmological constant (Λ) to be negative, and it becomes less negative with time, changing at a gradually decreasing rate. The dependence of pressure of the all-pervading cosmic fluid upon density, corresponding to the fifth dimension, has been described in terms of a skewness parameter (δ) which comes out to be decreasing with time. The anisotropy factor has been calculated in this study, whose numerical value has been found to be decreasing with time, indicating a journey of the universe towards phases of gradually smaller anisotropy.

Moduli dynamics in effective nested warped geometry in four dimensions and some cosmological implications

We analyze the effective four-dimensional dynamics of the extra-dimensional moduli fields in curved braneworlds having nested warping, with particular emphasis on the doubly warped model which is interesting in the light of current collider constraints on the mass of the Kaluza-Klein graviton. The presence of a non-zero brane cosmological constant (Ω) naturally induces an effective moduli potential in the four-dimensional action, which shows distinct features in dS (Ω > 0) and AdS (Ω < 0) branches. For the observationally interesting case of dS 4-branes, a metastable minimum in the potential arises along the first modulus, with no minima along the higher moduli. The underlying nested geometry also leads to interesting separable forms of the non-canonical kinetic terms in the Einstein frame, where the brane curvature directly impacts the kinetic properties of only the first modulus. The non-canonicity of the scenario has been illustrated via an explicit computation of the field space curvature. We subsequently explore the ability of curved multiply warped geometries to drive inflation with an in-built exit mechanism, by considering predominant slow roll along each modular direction on a case-by-case basis. We find slow roll on top of the metastable plateau along the first modular direction to be the most viable scenario, with the higher-dimensional moduli parametrically tuning the height of the potential without significant impact on the inflationary observables. On the other hand, while slow roll along the higher moduli can successfully inflate the background and eventually lead to an exit, consistency with observations seemingly requires unphysical hierarchies among the extra-dimensional radii, thus disfavouring such scenarios.

Cosmological constraints on curved quintessence

Dynamical dark energy has gained renewed interest due to recent theoretical and observational developments. In the present paper, we focus on a string-motivated dark energy set-up, and perform a detailed cosmological analysis of exponential quintessence with potential V = V 0 e λϕ -, allowing for non-zero spatial curvature. We first gain some physical intuition into the full evolution of such a scenario by analysing the corresponding dynamical system. Then, we test the model using a combination of Planck CMB data, DESI BAO data, as well as recent supernovae datasets. For the model parameter λ, we obtain a preference for nonzero values: λ = 0.48+0.28 -0.21, 0.68+0.31 -0.20, 0.77+0.18 -0.15 at 68% C.L. when combining CMB+DESI with Pantheon+, Union3 and DES-Y5 supernovae datasets respectively. We find no significant hint for spatial curvature. We discuss the implications of current cosmological results for the exponential quintessence model, and more generally for dark energy in string theory.

Refining Euclidean Obfuscatory Nodes Helps: A Joint-Space Graph Learning Method for Graph Neural Networks.

Many graph neural networks (GNNs) are inapplicable when the graph structure representing the node relations is unavailable. Recent studies have shown that this problem can be effectively solved by jointly learning the graph structure and the parameters of GNNs. However, most of these methods learn graphs by using either a Euclidean or hyperbolic metric, which means that the space curvature is assumed to be either constant zero or constant negative. Graph embedding spaces usually have nonconstant curvatures, and thus, such an assumption may produce some obfuscatory nodes, which are improperly embedded and close to multiple categories. In this article, we propose a joint-space graph learning (JSGL) method for GNNs. JSGL learns a graph based on Euclidean embeddings and identifies Euclidean obfuscatory nodes. Then, the graph topology near the identified obfuscatory nodes is refined in hyperbolic space. We also present a theoretical justification of our method for identifying obfuscatory nodes and conduct a series of experiments to test the performance of JSGL. The results show that JSGL outperforms many baseline methods. To obtain more insights, we analyze potential reasons for this superior performance.

Exponential quintessence: curved, steep and stringy?

We explore the possibility that our universe’s current accelerated expansion is explained by a quintessence model with an exponential scalar potential, V = V0e−λ ϕ, keeping an eye towards λ ≥ 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{2} $$\\end{document} and an open universe, favorable to a string theory realisation and with no cosmological horizon. We work out the full cosmology of the model, including matter, radiation, and optionally negative spatial curvature, for all λ > 0, performing an extensive analysis of the dynamical system and its phase space. The minimal physical requirements of a past epoch of radiation domination and an accelerated expansion today lead to an upper bound λ ≲ 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{3} $$\\end{document}, which is driven slightly up in the presence of observationally allowed spatial curvature. Cosmological solutions start universally in a kination epoch, go through radiation and matter dominated phases and enter an epoch of acceleration, which is only transient for λ > 2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{2} $$\\end{document}. Field distances traversed between BBN and today are sub-Planckian. We discuss possible string theory origins and phenomenological challenges, such as time variation of fundamental constants. We provide theoretical predictions for the model parameters to be fitted to data, most notably the varying dark energy equation of state parameter, in light of recent results from DES-Y5 and DESI.

Constraint on the Cosmic Curvature in a Model with the Schwarzschild–de Sitter Metric from Supernovae and Gamma-Ray Burst Observational Data

In developing his cosmological model of 1917, de Sitter theoretically predicted the phenomenon of cosmological redshift (the de Sitter effect), which he did long before the discovery of this phenomenon in observations. The de Sitter effect is gravitational by its nature, as it is due to differences between the coordinate systems of the observer and the distant source. However, the relationship between the redshift and distance derived from the de Sitter metric is at odds with observations, since this relationship is nonlinear (quadratic) for small redshifts, while the observed relationship between the same quantities is strictly linear. This paper discusses the possibility that cosmological redshift is gravitational by its nature, as in de Sitter’s 1917 model. At the same time, here, as in de Sitter’s model, an elliptical space is used, the main characteristic of which is the identification of its antipodal points. But, unlike de Sitter’s model, here, in order to ensure strict linear dependence of the redshift on distance, the origin of the reference system is transferred to the observer’s antipodal point. The Schwarzschild–de Sitter metric used in this model allows you to estimate the curvature of space from observational data. To achieve this, a theoretical Hubble diagram is built within the framework of the model with the Schwarzschild–de Sitter metric, which is compared with observations from the Pantheon+ catalogue of type Ia supernovae and the Amati catalogue of gamma-ray bursts in the redshift range of 0&lt;z&lt;8. As a result of this comparison, we found that the lower estimate of the radius of curvature of space was quite large: 2.4×1015 Mpc. This means that the observational data indicate a negligible curvature of space.

EINSTEINS THEORY OF RELATIVITY AND ORGANIZATIONAL FLEXIBILITY IN DIGITAL TRANSFORMATIONS

The paper will illustrate an analogy of Einsteins Theory of Relativity with the features of organizational flexibility against the backdrop of digital transformations. The relativity of space-time on the structures of organizations in their dynamics has informed the research. Explain how principles of relativity time dilations and space curvatures can be applied in organizational adaptability and responsiveness to give insight on how such flexibility may be achieved in the organisations, especially during digital disruptions. The findings suggest that much like how relativity reset peoples understanding of physics, the flexible approach toward organizational change can reset success in the digital age.

Constraints on the parameters of modified Chaplygin–Jacobi and modified Chaplygin–Abel gases in f(T) gravity

In this work, we explore the parameter constraints of two dark energy models, namely the Modified Chaplygin–Jacobi gas (MCJG) and Modified Chaplygin–Abel gas (MCAG), within the context of [Formula: see text] gravity model in a non-flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Our investigation involves comparing the equation of state for the MCJG and MCAG dark energy models with the equation of state derived from the [Formula: see text] gravity model. To derive constraints for the dark energy and [Formula: see text] gravity models, we use recent astronomical datasets, including [Formula: see text] data, type Ia supernovae observations, Gamma Ray Bursts data, quasar data, and Baryon Acoustic Oscillation (BAO) measurements. We present the reduced Hubble parameter in terms of observable parameters such as [Formula: see text] (density parameter of radiation), [Formula: see text] (density parameter of dark matter), [Formula: see text] (density parameter associated with spatial curvature), [Formula: see text] (density parameter of Modified Chaplygin–Jacobi gas), [Formula: see text] (density parameter of Modified Chaplygin–Abel gas), and [Formula: see text] (present value of the Hubble parameter). We explore the cosmological evolution through various cosmic diagnostic parameters, including the deceleration parameter, [Formula: see text] diagnostic, and statefinder diagnostic pair [Formula: see text]. These diagnostic parameters offer valuable insights into the expansion dynamics and the nature of dark energy in the universe. We have also assessed the viability of the models using the information criteria. Our aim is to shed light on the nature of dark energy and its connection to the [Formula: see text] gravity model, and ultimately gain a deeper understanding of the underlying mechanisms driving the accelerated expansion of our universe.