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LIU, HONGYA, HUANYING LIU, BAORONG CHANG, and LIXIN XU. "INDUCED PHANTOM AND 5D ATTRACTOR SOLUTION IN SPACETIME–MATTER THEORY." Modern Physics Letters A 20, no. 26 (2005): 1973–81. http://dx.doi.org/10.1142/s0217732305017366.
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In Spacetime–Matter theory we assume that the 4D induced matter of the 5D Ricci-flat bouncing cosmological solutions contains a perfect fluid as well as an induced scalar field. Then we show that the conventional 4D quintessence and phantom models of dark energy could be recovered from the 5D cosmological solutions. By using the phase-plane analysis to study the stability of evolution of the 5D models, we find that the conventional 4D late-time attractor solution is also recovered. This attractor solution shows that the scale factors of the phantom dominated universes in both the 4D and 5D theories will reach infinity in a finite time and the universes will be ended at a new kind of spacetime singularity at which everything will be annihilated. We also find that the repulsive force of the phantom may provide us with a mechanics to explain the bounce.
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Hieu, Tran Minh. "A Model of Bulk Supersymmetry in Warped Spacetime." Communications in Physics 26, no. 2 (2016): 111. http://dx.doi.org/10.15625/0868-3166/26/2/8461.
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The Randall-Sundrum solution to the hierarchy problem in the brane-world scenario has made a significant impact on the development of model building.We investigate in this paper a model of supersymmetry in a 5D spacetime with the Randal-Sundrum warped metric.The minimal supersymmetric extension of the standard model (MSSM) superfields propagate in the bulk between the UV and IR branes at separated orbifold fixed points, while the hidden sector in charge of supersymmetry breaking is confined on the UV brane.We derive the 4D effective action from the original 5D action of the underlying theory.The effective 4D Yukawa couplings and all the soft supersymmetry breaking terms are calculated in terms of the 5D theory's coefficients. We comment on the important role of the bulk mass parameter in the relation with the geometrical properties of particles.
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Land, Martin. "Weak Gravitation in the 4+1 Formalism." Universe 8, no. 3 (2022): 185. http://dx.doi.org/10.3390/universe8030185.
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The 4+1 formalism in general relativity (GR) prescribes field equations for the spacetime metric γμνx,τ which is local in the spacetime coordinates x and evolves according to an external “worldtime” τ. This formalism extends to GR the Stueckelberg Horwitz Piron (SHP) framework, developed to address the various issues known as the problem of time as they appear in electrodynamics. SHP field theories exhibit a formal 5D symmetry on (x,τ) that is strategically broken to 4+1 representations of the Lorentz group, resulting in a manifestly covariant canonical formalism describing the τ-evolution of spacetime structures as an initial value problem. Einstein equations for γμνx,τ are found by constructing a 5D pseudo-manifold (combining 4D geometry and τ-dynamics) and performing the natural foliation under broken 5D symmetry. This paper discusses weak gravitation in the 4+1 formalism, demonstrating the natural decomposition of the field equations into first-order evolution equations for the unconstrained 4D metric, and the propagation of constraints associated with the Bianchi identity.
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IOFA, MIKHAIL Z. "SECOND VARIATION OF INDUCED CURVATURE TERM IN BRANE-WORLD ACTION." Modern Physics Letters A 25, no. 06 (2010): 431–36. http://dx.doi.org/10.1142/s0217732310032512.
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In a 5D spacetime with a 3-brane embedded we calculate the second variation of the scalar 4D curvature term on the brane under variations of the 5D metric. It is shown that the second variation of the 4D scalar curvature term in adapted coordinates is expressed only through variations of the components of the 5D metric with 4D indices.
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GOGBERASHVILI, MERAB, and DOUGLAS SINGLETON. "ANTI-DE SITTER ISLAND-UNIVERSES FROM 5D STANDING WAVES." Modern Physics Letters A 25, no. 25 (2010): 2131–43. http://dx.doi.org/10.1142/s021773231003358x.
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We construct simple standing wave solutions in a 5D spacetime with a ghost-like scalar field. The nodes of these standing waves are "islands" of 4D anti-de Sitter spacetime. In the case of increasing (decreasing) warp factor, there are a finite (infinite) number of nodes and thus a finite (infinite) number of anti-de Sitter island-universes having different gravitational and cosmological constants. This is similar to the landscape models, which postulate a large number of universes with different parameters.
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SLAGTER, REINOUD JAN, and DERK MASSELINK. "WARPED SELF-GRAVITATING U(1) GAUGE COSMIC STRINGS IN 5D." International Journal of Modern Physics D 21, no. 07 (2012): 1250060. http://dx.doi.org/10.1142/s0218271812500605.
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We present the "classical" Nielsen–Olesen vortex solution on a warped 5-dimensional spacetime, where we solved the effective 4-dimensional equations from the 5-dimensional equations together with the junction and boundary conditions. 4-dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, Gμ ≤ 10-6. Moreover, there is no observational evidence of axially symmetric lensing effect caused by cosmic strings. Also super-massive cosmic strings (Gμ ≳ 1), predicted by superstring theory, possess some problems. They are studied because the universe may have undergone phase transitions at scales much higher than the GUT scale. But Gμ ≳ 1 is far above observational bounds, so one needs an inflationary scenario to smooth them out. Further, it is believed that these super-massive strings never extended to macroscopic size. Brane world models could overcome these problems. Gμ could be warped down to GUT scale, even if its value was at the Planck scale. In our warped cosmic string model, where the string mass per unit length in the bulk can be of order of the Planck scale, we find that the 4-dimensional brane spacetime is exponential warped down. Moreover, asymptotically the induced 4-dimensional spacetime does not show conical behavior. So there is no angle deficit compared to its value in the bulk and the spacetime seems to be unphysical, at least under fairly weak assumptions on the stress–energy tensor and without a positive brane tension. The results are confirmed by numerical solutions of the field equations.
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Land, Martin. "A vielbein formalism for SHP general relativity." Journal of Physics: Conference Series 2482, no. 1 (2023): 012006. http://dx.doi.org/10.1088/1742-6596/2482/1/012006.
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Abstract The 4+1 formalism in general relativity expresses the Einstein equations as a manifestly covariant initial value problem, resulting in a pair of first order evolution equations for the metric γμv and intrinsic curvature Kμv of spacetime geometry (μ, v = 0, 1, 2, 3). This approach extends the Stueckelberg-Horwitz-Piron (SHP) framework, a covariant approach to canonical particle mechanics and field theory employing a Lorentz scalar Hamiltonian K and an external chronological parameter τ. The SHP Hamiltonian generates τ-evolution of spacetime events xμ (τ) or ψ (x, τ) in an a priori unconstrained phase space; standard relativistic dynamics can be recovered a posteriori by imposing symmetries that express the usual mass shell constraint for individual particles and fields as conservation laws. As a guide to posing field equations for the evolving metric, we generalize the structure of SHP electrodynamics, with particular attention to O(3,1) covariance. Thus, the 4+1 method first defines a 5D pseudo-spacetime as a direct product of spacetime geometry and chronological evolution, poses 5D field equations whose symmetry must be broken to 4D, and then implements the implied 4+1 foliation to obtain evolution equations. In this paper, we sharpen and clarify the interpretation of this decomposition by introducing a fixed orthonormal quintrad frame and a 5D vielbein field that by construction respects the preferred 4+1 foliation. We show that for any diagonal metric, this procedure enables the evolution equation for the metric to be replaced by an evolution equation for the vielbein field itself, simplifying calculation of the spin connection and curvature.
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Chiang, Kwan C. "Anatomy of spacetime and possible origins of internal symmetry and all particle quantum numbers." Physics Essays 33, no. 3 (2020): 342–47. http://dx.doi.org/10.4006/0836-1398-33.3.342.
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Not driven by observations, this paper digs into the “internal workings” of spacetime. Through logical deductions, micro dimensions appear to be uncovered, with possible SU(4) or SU(5): 1. It is thought that special relativity merely initiated the definition of spacetime, but more scales are yet to be defined. 2. In the definition of spacetime, EM (electromagnetism) played another critical role, i.e., the six circular magnetic and electric field lines (running on the six planes) cross and “define equivalencies” between the four linear scales. Without this definition, light would not be measured at the same speed in different directions. Being a gauge theory, EM defines two things: Linear scales and “equivalencies” between linear scales. 3. For any scale (and their equivalencies), there could be no or many arbitrarily assumed definitions, or a concrete definition based on relevant physics. Nature would conform with but the one based on relevant physics, because Nature itself is consisted of that relevant physics. Thus, the principle: No scale and their equivalencies are meaningful unless defined by relevant physics. 4. Then, what are those fields running (and defining equivalencies between the six “angle scales”) on the six planes of the 4D spacetime? It is believed to be the “classical” weak fields which run in solid angles (or “3D angles”) between the six planes. (The only suspicion is that this rotation does not preserve vector length, which is not a problem ultimately.) 5. If the six angle scales are drawn as six axes of a 6D superspace, then the “3D angle” rotations look like “plane angle” rotations and cause SO(6)∼SU(4) [or SO(10)∼SU(5) for 5D spacetime], which appears to match baryon spectrum without quarks. 6. Since this rotation is between “planes” of the “external” spacetime, no linear dimension is visible, yet causing P-violations. 7. Similarly, fields running in 4D and 5D angle rotations (between 3D and 4D surfaces) must also exist, which may be responsible for CP-violation and strong interactions. 8. The 5D angle rotations may be generating Baryon and Lepton numbers and hence explaining their conservation behaviors, e.g., no proton decay. 9. It can be inferred, if 3D, 4D (and 5D) angle rotation fields did not exist, the 4D (and 5D) spacetime would be warped and the four (or five) linear axes would not be perpendicular to each other. 10. EM was simplified and turned elegant “only” after redefinition of spacetime by special relativity. Likewise, weak, CP-violation and strong interactions are expected to simplify and turn as elegant as EM when 2D (plane), 3D, and 4D angle scales are defined by weak, CP-violation, and strong forces, respectively. 11. Verifications as accurate as EM are expected too. 12. Mathematically, higher angle rotations thought to be inexistent only because it does not conserve vector length. Actually, they did not vanish and their symmetries would surface in particle classifications when linear momentum is not concerned. Micro dimensions being invisible is because symmetries do not have to happen between linear axes, but can happen between 2-, 3- or 4-surfaces. These geometries together generate the complete particles spectrum.
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Cho, Inyong, Gungwon Kang, Sang Pyo Kim, and Chul H. Lee. "Spacetime Structure of 5D Hypercylindrical Vacuum Solutions with Tension." Journal of the Korean Physical Society 53, no. 9(2) (2008): 1089–94. http://dx.doi.org/10.3938/jkps.53.1089.
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Dao, H. L. "Cosmological solutions from 5D N = 4 matter-coupled supergravity." Journal of Physics Communications 6, no. 2 (2022): 025003. http://dx.doi.org/10.1088/2399-6528/ac4fb0.
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Abstract From five-dimensional N = 4 matter-coupled gauged supergravity, smooth time-dependent cosmological solutions, connecting a dS 5−d × H d (with d = 2, 3) spacetime at early times to a dS 5 spacetime at late times, are presented. The solutions are derived from the second-order equations of motion arising from all the gauged theories that can admit dS 5 solutions. There are eight such theories constructed from gauge groups of the form SO(1, 1) × G nc and SO ( 1 , 1 ) diag ( n ) × G nc , with n = 2, 3, where G nc is a non-compact gauge factor whose compact part must be embedded entirely in the matter symmetry group of 5D matter-coupled supergravity. Furthermore, we analyze how the cosmological solutions and their corresponding dS 5 vacua cannot arise from the first-order equations that solve the second-order field equations.
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DZHUNUSHALIEV, V. D. "SPHERICALLY SYMMETRIC SOLUTION FOR TORSION AND THE DIRAC EQUATION IN 5D SPACETIME." International Journal of Modern Physics D 07, no. 06 (1998): 909–15. http://dx.doi.org/10.1142/s0218271898000590.
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Torsion in a 5D spacetime is considered. In this case, gravitation is defined by the 5D metric and the torsion. It is conjectured that torsion is connected with a spinor field. In this case, Dirac's equation becomes the nonlinear Heisenberg equation. It is shown that this equation has a discrete spectrum of solutions with each solution being regular on the whole space and having finite energy. Every solution is concentrated on the Planck region and hence we can say that torsion should play an important role in quantum gravity in the formation of bubbles of spacetime foam. On the basis of the algebraic relation between torsion and the classical spinor field in Einstein–Cartan gravity, the geometrical interpretation of the spinor field is considered as "the square root" of torsion.
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El-Nabulsi, Rami Ahmad. "Five-dimensional Brans–Dicke compactified universe dominated by a varying speed of light." Modern Physics Letters A 35, no. 30 (2020): 2050252. http://dx.doi.org/10.1142/s0217732320502521.
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We extend the model of a 5D Brans–Dicke gravity theory reduced to 4D through the presence of a hypersurface-orthogonal space-like killing vector field in the underlying 5D spacetime by including a varying speed of light. The resulting model is characterized by the presence of two scalar fields. We focus on late-time power law solutions which emerge in general when scalar fields couple to spacetime curvature and do not contradict the SNIa astrophysical data. Analytic solutions in 4-dimensions are derived and late-time accelerated expansion was found. The universe is dominated by dark energy, free from phantom field and is characterized by a decaying energy matter density, decaying scalar fields, and a decreasing celerity of light. The model is confronted with astrophysical observations and is found to fit these data.
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Kuniyal, Ravi Shankar, Hemwati Nandan, Uma Papnoi, Rashmi Uniyal, and K. D. Purohit. "Strong lensing and observables around 5D Myers–Perry black hole spacetime." Modern Physics Letters A 33, no. 23 (2018): 1850126. http://dx.doi.org/10.1142/s0217732318501262.
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We study the motion of massless test particles in a five-dimensional (5D) Myers–Perry black hole spacetime with two-spin parameters. The behavior of the effective potential in view of different values of black hole parameters is discussed in the equatorial plane. The frequency shift of photons is calculated which is found to depend on the spin parameter of black hole and the observed redshift is discussed accordingly. The deflection angle and the strong deflection limit coefficients are also calculated and their behavior with the spin parameters is analyzed in detail. It is observed that the behaviors of both deflection angle and strong field coefficient differs from Kerr black hole spacetime in four dimensions in General Relativity (GR), which is mainly due to the presence of two-spin parameters in higher dimension.
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DZHUNUSHALIEV, V. "AN APPROXIMATE MODEL OF THE SPACETIME FOAM." International Journal of Modern Physics D 11, no. 03 (2002): 299–310. http://dx.doi.org/10.1142/s0218271802001639.
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An approximate model of the spacetime foam is offered in which a quantum handle (wormhole) is a 5D wormhole-like solution. Neglecting the linear sizes of the wormhole throat we can introduce a spinor field for an approximate and effective description of the foam. The definition of the spinor field can be made by a dynamic and nondynamic ways. In the first case some field equations are used and the second case leads to superspace. It is shown that the spacetime with the foam is similar to a dielectric with dipoles and supergravity theories with a nonminimal interaction between spinor and electromagnetic fields can be considered as an effective model for the spacetime foam.
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Wu, Ya-Bo, Yue-Yue Zhao, Jian-Bo Lu, Jian Li, Wen-Xin Zhang, and Hong Chang. "The Generalized f ( R ) Model with Coupling in 5D Spacetime." Chinese Physics Letters 30, no. 6 (2013): 069801. http://dx.doi.org/10.1088/0256-307x/30/6/069801.
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SHANKAR, KARTHIK H., and KAMESHWAR C. WALI. "KALUZA–KLEIN THEORY WITH TORSION CONFINED TO THE EXTRA DIMENSION." Modern Physics Letters A 25, no. 25 (2010): 2121–30. http://dx.doi.org/10.1142/s0217732310033566.
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Here we consider a variant of the five-dimensional Kaluza–Klein (KK) theory within the framework of Einstein–Cartan formalism that includes torsion. By imposing a set of constraints on torsion and Ricci rotation coefficients, we show that the torsion components are completely expressed in terms of the metric. Moreover, the Ricci tensor in 5D corresponds exactly to what one would obtain from torsion-free general relativity on a 4D hypersurface. The contributions of the scalar and vector fields of the standard KK theory to the Ricci tensor and the affine connections are completely nullified by the contributions from torsion. As a consequence, geodesic motions do not distinguish the torsion free 4D spacetime from a hypersurface of 5D spacetime with torsion satisfying the constraints. Since torsion is not an independent dynamical variable in this formalism, the modified Einstein equations are different from those in the general Einstein–Cartan theory. This leads to important cosmological consequences such as the emergence of cosmic acceleration.
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Paiman, Mechid, Horia Cornean, and Christoph Köhn. "Schwarzschild Black Holes in Extended Spacetime with Two Time Dimensions." Astronomy 2, no. 4 (2023): 269–85. http://dx.doi.org/10.3390/astronomy2040018.
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Black holes are one of the most extreme phenomena in the Universe, bridging the gap between the realms of general relativity and quantum physics. Any matter that crosses the event horizon moves towards the core of the black hole, creating a singularity with infinite mass density—a phenomenon that cannot be comprehended within present theories of relativity and quantum physics. In this study, we undertake an investigation of non-rotating, non-charged Schwarzschild black holes in an extended spacetime framework with two time dimensions. To accomplish this, we extend Einstein’s field equations by one more temporal dimension. We solve the corresponding equations for a spherical central mass, which leads to an Abel-type equation for the 5D Schwarzschild metric. By exploring distinct solution classes, we present an approximate solution for the 5D metric. Our proposed solution maintains consistency with Schwarzschild’s 4D solution. Finally, we address the central black hole singularity and demonstrate a potential breakthrough, as our solution effectively avoids the singularity quandary, providing valuable insight into the fundamental properties of black holes in this augmented framework.
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Chkareuli, J. L., and Z. Kepuladze. "Emergent Yang–Mills theories from universal extra dimensions." Modern Physics Letters A 32, no. 05 (2017): 1750029. http://dx.doi.org/10.1142/s0217732317500298.
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We study emergent Yang–Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (4D) gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang–Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories, an internal symmetry also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.
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Kyae, Bumseok. "Einstein Gravity on a Brane in 5D Non-compact Flat Spacetime." Journal of High Energy Physics 2004, no. 03 (2004): 038. http://dx.doi.org/10.1088/1126-6708/2004/03/038.
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Ahmed, Nasr, and H. Rafat. "Topological origin of holographic principle: Application to wormholes." International Journal of Geometric Methods in Modern Physics 15, no. 08 (2018): 1850131. http://dx.doi.org/10.1142/s0219887818501311.
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In this paper, we suggest a mathematical representation to the holographic principle through the theory of topological retracts. We found that the topological retraction is the mathematical analog of the hologram idea in modern quantum gravity and it can be used to explore the geometry of the hologram boundary. An example has been given on the five-dimensional (5D) wormhole spacetime [Formula: see text] which we found can retract to lower-dimensional circles [Formula: see text]. In terms of the holographic principle, the description of this volume of spacetime [Formula: see text] is encoded on the lower-dimensional circle which is the region boundary.
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WESSON, PAUL S. "MASS, PARTICLES AND WAVES IN HIGHER DIMENSIONS." International Journal of Modern Physics D 12, no. 09 (2003): 1721–27. http://dx.doi.org/10.1142/s0218271803004146.
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Using 5D membrane/induced-matter theory as a basis, we derive the equations of motion for a novel gauge. The latter admits both particle and wave behaviour, as well as super-communication (wherein there is causal contact in the higher-dimensional manifold among points which are disjoint in spacetime). Possible ways to test this model are suggested, notably using particle mass.
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Zaregonbadi, Raziyeh. "Cosmic acceleration via space-time-matter theory." Modern Physics Letters A 34, no. 36 (2019): 1950296. http://dx.doi.org/10.1142/s0217732319502961.
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We consider the space-time-matter theory (STM) in a 5D vacuum spacetime with a generalized FLRW metric to investigate the late-time acceleration of the universe. For this purpose, we derive the 4D induced field equations and obtain the evolution of the state parameter with respect to the redshift. Then, we show that with consideration of the extra dimension scale factor to be a linear function of redshift, this leads to a model which gives an accelerating phase in the universe. Moreover, we derive the geodesic deviation equation in the STM theory to study the relative acceleration of the parallel geodesics of this spacetime, and also, obtain the observer area-distance as a measurable quantity to compare this theory with two other models.
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Land, Martin. "A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric." Symmetry 12, no. 10 (2020): 1721. http://dx.doi.org/10.3390/sym12101721.
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We propose a field theory for the local metric in Stueckelberg–Horwitz–Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines xμτ (μ=0,1,2,3) is parameterized by an external time τ. Combining insights from SHP electrodynamics and the ADM formalism in general relativity, we generalize the notion of a 4D spacetime M to a formal manifold M5=M×R, representing an admixture of geometry (the diffeomorphism invariance of M) and dynamics (the system evolution of Mτ with the monotonic advance of τ∈R). Strategically breaking the formal 5D symmetry of a metric gαβ(x,τ) (α,β=0,1,2,3,5) posed on M5, we obtain ten unconstrained Einstein equations for the τ-evolution of the 4D metric γμν(x,τ) and five constraints that are to be satisfied by the initial conditions. The resulting theory differs from five-dimensional (5D) gravitation, much as SHP U(1) gauge theory differs from 5D electrodynamics.
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Wesson, Paul S. "The status of modern five-dimensional gravity (A short review: Why physics needs the fifth dimension)." International Journal of Modern Physics D 24, no. 01 (2014): 1530001. http://dx.doi.org/10.1142/s0218271815300013.
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Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification in regard to string theory, but is misguided as applied to five-dimensional (5D) theories with a large extra dimension. Such theories smoothly embed general relativity, ensuring recovery of the latter's observational support. When the embedding of spacetime is carried out in accordance with Campbell's theorem, the resulting 5D theory naturally explains the origin of classical matter and vacuum energy. Also, constraints on the equations of motion near a high-energy surface or membrane in the 5D manifold lead to quantization and quantum uncertainty. These are major returns on the modest investment of one extra dimension. Instead of fruitless bickering about whether it is possible to "see" the fifth dimension, it is suggested that it be treated on par with other concepts of physics, such as time. The main criterion for the acceptance of a fifth dimension (or not) should be its usefulness.
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LIU, MOLIN, HONGYA LIU, LIXIN XU, and PAUL S. WESSON. "RADIATION AND POTENTIAL BARRIERS OF A 5D BLACK STRING SOLUTION." Modern Physics Letters A 21, no. 39 (2006): 2937–45. http://dx.doi.org/10.1142/s0217732306022341.
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By using a massless scalar field we examine the effect of an extra dimension on black hole radiation. As the equations are coupled, we find that the structure of the fifth dimension (as for membrane and induced-matter theory) affects the nature of the radiation observed in four-dimensional spacetime. In the case of the Schwarzschild–de Sitter solution embedded in a Randall–Sundrum brane model, the extension of the black hole along the fifth dimension looks like a black string. Then it is shown that, on the brane, the potential barrier surrounding the black hole has a quantized as well as a continuous spectrum. In principle, Hawking radiation may thus provide a probe for higher dimensions.
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PONCE DE LEON, J. "REINVENTING SPACETIME ON A DYNAMICAL HYPERSURFACE." Modern Physics Letters A 21, no. 12 (2006): 947–59. http://dx.doi.org/10.1142/s0217732306020214.
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In braneworld models, Spacetime-Matter and other Kaluza–Klein theories, our spacetime is devised as a four-dimensional hypersurface orthogonal to the extra dimension in a five-dimensional bulk. We show that the FRW line element can be "reinvented" on a dynamical four-dimensional hypersurface, which is not orthogonal to the extra dimension, without any internal contradiction. This hypersurface is selected by the requirement of continuity of the metric and depends explicitly on the evolution of the extra dimension. The main difference between the "conventional" FRW, on an orthogonal hypersurface, and the new one is that the latter contains higher-dimensional modifications to the regular matter density and pressure in 4D. We compare the evolution of the spacetime in these two interpretations and find that a wealth of "new" physics can be derived from a five-dimensional metric if it is interpreted on a dynamical (non-orthogonal) 4D hypersurface. In particular, in the context of a well-known cosmological metric in 5D, we construct a FRW model which is consistent with the late accelerated expansion of the universe, while fitting simultaneously the observational data for the deceleration parameter. The model predicts an effective equation of state for the universe, which is consistent with observations.
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WESSON, PAUL S. "IS MASS QUANTIZED?" Modern Physics Letters A 19, no. 26 (2004): 1995–2000. http://dx.doi.org/10.1142/s0217732304015270.
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The cosmological constant combined with Planck's constant and the speed of light implies a quantum of mass of approximately 2×10-65 g . This follows either from a generic dimensional analysis, or from a specific analysis where the cosmological constant appears in 4D spacetime as the result of a dimensional reduction from higher-dimensional relativity (such as 5D induced-matter and membrane theory). In the latter type of theory, all the particles in the universe can be in higher-dimensional contact.
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Crispim, Tiago M., Milko Estrada, C. R. Muniz, and G. Alencar. "Braneworld black bounce to transversable wormhole." Journal of Cosmology and Astroparticle Physics 2024, no. 10 (2024): 063. http://dx.doi.org/10.1088/1475-7516/2024/10/063.
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Abstract We provide a way for embedding a 4-dimensional geometry corresponding to the Simpson-Visser (SV) spacetime — which is capable of representing a traversable wormhole, a one-way wormhole, or a regular black hole — into a Randall-Sundrum setup. To achieve this, we linearly deform the bulk geometry and the bulk matter distribution concerning a coupling constant. These deformations induce a transition from a 5D vacuum AdS state to an anisotropic matter distribution. The latter results in the induced geometry on the brane transitioning from a singular Schwarzschild spacetime to a regularized SV spacetime. Since there are no sources or matter fields on the brane, we can assert that the induced SV geometry on the brane arises from the influence of geometrical and matter deformations in the bulk. Thus, the central singularity is suppressed. We determine the cases where the energy conditions are either satisfied or violated. Our spacetime is asymptotically radial AdS, which is intriguing given the absence of a global AdS box that would prevent instability under larger wavelength perturbations. Therefore, it is no longer appropriate to claim that instability exists for very small perturbations near the AdS horizon. Thus, we propose that the stability of the solution can be analyzed by examining the speed of sound due to the presence of matter fields in the energy momentum tensor.
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Sánchez, Pablo Alejandro, and Mauricio Bellini. "Primordial Dark Energy from a Condensate of Spinors in a 5D Vacuum." Advances in High Energy Physics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/789476.
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We explore the possibility that the expansion of the universe can be driven by a condensate of spinors which are free of interactions in a 5D relativistic vacuum defined in an extended de Sitter spacetime which is Riemann flat. The extra coordinate is considered as noncompact. After making a static foliation on the extra coordinate, we obtain an effective 4D (inflationary) de Sitter expansion which describes an inflationary universe. We found that the condensate of spinors studied here could be an interesting candidate to explain the presence of dark energy in the early universe. The dark energy density which we are talking about is poured into smaller subhorizon scales with the evolution of the inflationary expansion.
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Okada, Nobuchika, Digesh Raut, and Desmond Villalba. "Domain-Wall Standard Model in non-compact 5D and LHC phenomenology." Modern Physics Letters A 34, no. 10 (2019): 1950080. http://dx.doi.org/10.1142/s0217732319500809.
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We propose a framework to construct “Domain-Wall Standard Model” in a non-compact 5-dimensional spacetime, where all the Standard Model (SM) fields are localized in certain domains of the 5th dimension and the SM is realized as a 4-dimensional effective theory without any compactification for the 5th dimension. In this context, we investigate the collider phenomenology of the Kaluza–Klein (KK) modes of the SM gauge bosons and the current constraints from the search for a new gauge boson resonance at the Large Hadron Collider Run-2. The couplings of the SM fermions with the KK-mode gauge bosons depend on the configuration of the SM fermions in the 5-dimensional bulk. This “geometry” of the model can be tested at the future Large Hadron Collider experiment, once a KK-mode of the SM gauge boson is discovered.
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SÁNCHEZ, PABLO ALEJANDRO, and MAURICIO BELLINI. "INFLATIONARY DARK ENERGY FROM A CONDENSATE OF SPINORS IN A 5D VACUUM." International Journal of Modern Physics D 22, no. 12 (2013): 1342028. http://dx.doi.org/10.1142/s0218271813420285.
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What is the physical origin of dark energy? Could this energy be originated by other fields than the inflaton? In this paper, we explore the possibility that the expansion of the universe can be driven by a condensate of spinors. These spinors are free of interactions on five-dimensional (5D) relativistic vacuum in an extended de Sitter spacetime. The extra coordinate is considered as noncompact. After making a static foliation on the extra coordinate, we obtain an effective four-dimensional (4D) (inflationary) de Sitter expansion which describes an inflationary universe. In view of our results, we conclude that the condensate of spinors here studied could be an interesting candidate to explain the presence of dark energy in the early universe.
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Gogberashvili, Merab. "Conformal (2 + 4)-braneworld." International Journal of Modern Physics D 26, no. 11 (2017): 1750125. http://dx.doi.org/10.1142/s0218271817501255.
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The 6D brane model is considered, where matter is trapped on the surface of a (2+4)-hyperboloid, as is suggested by the geometrical structure behind the 4D conformal group. The effective dimension of the bulk spacetime for matter fields is five, with the extra space-like and time-like domains. Using the embedding theory, the presence of the familiar factorizable 5D brane metrics in both domains is shown. These metrics with exponential warp factors are able to provide with the additional reduction of the effective spacetime dimensions down to four. It is demonstrated that the extra (1+1)-space is not simply connected and there is a gap in the range of the extra coordinates. This can explain the stability of the model in the domain with the time-like effective fifth dimension and the appearance of the cosmological constant due to the tachyon condensation. It is found that the model exhibits orbifold symmetry and thus is free from the fermion chirality problem.
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Oron, O., and L. P. Horwitz. "Eikonal approximation to 5D wave equations as geodesic motion in a curved 4D spacetime." General Relativity and Gravitation 37, no. 3 (2005): 491–506. http://dx.doi.org/10.1007/s10714-005-0038-7.
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Jasim, Mahmood Khalid, Sunil Kumar Maurya, Ksh Newton Singh, and Riju Nag. "Anisotropic Strange Star in 5D Einstein-Gauss-Bonnet Gravity." Entropy 23, no. 8 (2021): 1015. http://dx.doi.org/10.3390/e23081015.
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In this paper, we investigated a new anisotropic solution for the strange star model in the context of 5D Einstein-Gauss-Bonnet (EGB) gravity. For this purpose, we used a linear equation of state (EOS), in particular pr=βρ+γ, (where β and γ are constants) together with a well-behaved ansatz for gravitational potential, corresponding to a radial component of spacetime. In this way, we found the other gravitational potential as well as main thermodynamical variables, such as pressures (both radial and tangential) with energy density. The constant parameters of the anisotropic solution were obtained by matching a well-known Boulware-Deser solution at the boundary. The physical viability of the strange star model was also tested in order to describe the realistic models. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified TOV equation and the dynamical stability through the critical value of the radial adiabatic index. The mass-radius relationship was also established for determining the compactness and surface redshift of the model, which increases with the Gauss-Bonnet coupling constant α but does not cross the Buchdahal limit.
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EVANS, NICK. "RENORMALIZATION GROUP FLOWS IN THE DEFORMED ADS/CFT CORRESPONDENCE." International Journal of Modern Physics A 16, no. 11 (2001): 2027–33. http://dx.doi.org/10.1142/s0217751x01004657.
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In the AdS/CFT correspondence motion in the radial direction of the AdS space is identified with renormalization group flow in the field theory. For the N=4 Yang-Mills theory this motion is trivial. More interesting examples of renormalization group flow occur when the N=4 theory is deformed. Aspects of the flows are discussed for the N=4 theory on its moduli space, and deformed to N=2 in the infra-red within the context of 5d SUGRA. 10d lifts and brane probing are crucial tools for linking the spacetime backgrounds to the dual field theory.
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Stoica, O. C. "Kaluza theory with zero-length extra dimensions." International Journal of Modern Physics D 25, no. 11 (2016): 1640004. http://dx.doi.org/10.1142/s0218271816400046.
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A new approach to the Kaluza theory and its relation to the gauge theory is presented. Two degenerate metrics on the [Formula: see text]-dimensional total manifold are used, one corresponding to the spacetime metric and giving the fiber of the gauge bundle, and the other one to the metric of the fiber and giving the horizontal bundle of the connection. When combined, the two metrics give the Kaluza metric and its generalization to the non-Abelian case, justifying thus his choice. Considering the two metrics as fundamental rather than the Kaluza metric explains why Kaluza’s theory should not be regarded as five-dimensional (5D) vacuum gravity. This approach suggests that the only evidence of extra dimensions is given by the existence of the gauge forces, explaining thus why other kinds of evidence are not available. In addition, because the degenerate metric corresponding to the spacetime metric vanishes along the extra dimensions, the lengths in the extra dimensions is zero, preventing us to directly probe them. Therefore, this approach suggests that it is not justified to search for experimental evidence of the extra dimensions as if they are merely extra spacetime dimensions. On the other hand, the new approach uses a very general formalism, which can be applied to known and new generalizations of the Kaluza theory aiming to achieve more and make different experimental predictions.
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Sánchez, Pablo Alejandro, Mariano Anabitarte, and Mauricio Bellini. "Dirac equation for massive neutrinos in a Schwarzschild–de Sitter spacetime from a 5D vacuum." Physics Letters B 705, no. 5 (2011): 535–38. http://dx.doi.org/10.1016/j.physletb.2011.10.058.
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Dariescu, Marina–Aura, and Ciprian Dariescu. "An Exact Class of Bulk Field Potentials onto the 5D-Warp of de Sitter Spacetime." International Journal of Theoretical Physics 53, no. 9 (2014): 3239–45. http://dx.doi.org/10.1007/s10773-014-2121-x.
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LIU, HONGYA, and PAUL S. WESSON. "COSMOLOGICAL SOLUTIONS AND THEIR EFFECTIVE PROPERTIES OF MATTER IN KALUZA-KLEIN THEORY." International Journal of Modern Physics D 03, no. 03 (1994): 627–37. http://dx.doi.org/10.1142/s0218271894000769.
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We derive a “wave-like” class of exact cosmological solutions of the apparently empty 5D Kaluza-Klein field equations. Here by “wave-like” we mean that the solutions look like plane waves propagating in the fifth dimension. In the interpretation that the fifth dimension in Kaluza-Klein theory may induce matter in four dimensions, we then calculate the effective energy density ρ and pressure p, and study in detail the case for which the equation of state is p=γρ (where γ is an arbitrary constant). We show that for both the matter-dominated (γ=0) and radiation-dominated (γ=1/3) eras of the universe, the 4D spacetime defined by hypersurfaces of the 5D metrics are just the same as those of the standard Friedmann-Robertson-Walker models of general relativity. However, in our models the big bang is like a shock wave propagating along the fifth dimension, and different observers can measure different ages for the universe. This property may be tested using the spread in ages of astrophysical objects such as globular clusters.
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BILLYARD, ANDREW, PAUL S. WESSON, and DIMITRI KALLIGAS. "PHYSICAL ASPECTS OF SOLITONS IN (4+1) GRAVITY." International Journal of Modern Physics D 04, no. 05 (1995): 639–59. http://dx.doi.org/10.1142/s0218271895000430.
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The augmentation of general relativity’s spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from “conventional” relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the origin to the system is located and note that it can differ from the four-dimensional case. Furthermore, we study circular orbits and find that the 5D case is much richer; photons can have stable circular orbits in some instances, and stable orbits can exist right to the new origin in others. Finally, we derive both gravitational and inertial masses and find that they do not generally agree, although they can in a limiting case. For all three examinations, it is possible to obtain the four-dimensional results in one limiting case, that of the Schwarzschild solution plus a flat fifth dimension, and that the differences between 4D and 5D occur when the fifth dimension obtains any sort of significance.
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Singh, Ksh Newton, Piyali Bhar, Farook Rahaman, Neeraj Pant, and Mansur Rahaman. "Conformally non-flat spacetime representing dense compact objects." Modern Physics Letters A 32, no. 18 (2017): 1750093. http://dx.doi.org/10.1142/s0217732317500936.
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A new conformally non-flat interior spacetime embedded in five-dimensional (5D) pseudo Euclidean space is explored in this paper. We proceed our calculation with the assumption of spherically symmetric anisotropic matter distribution and Karmarkar condition (necessary condition for class one). This solution is free from geometrical singularity and well-behaved in all respects. We ansatz a new type of metric potential [Formula: see text] and solve for the metric potential [Formula: see text] via Karmarkar condition. Further, all the physical parameters are determined from Einstein’s field equations using the two metric potentials. All the constants of integration are determined using boundary conditions. Due to its conformally non-flat character, it can represent bounded configurations. Therefore, we have used it to model two compact stars Vela X-1 and Cyg X-2. Indeed, the obtained masses and radii of these two objects from our solution are well matched with those observed values given in [T. Gangopadhyay et al., Mon. Not. R. Astron. Soc. 431, 3216 (2013)] and [J. Casares et al., Mon. Not. R. Astron. Soc. 401, 2517 (2010)]. The equilibrium of the models is investigated from generalized TOV-equation. We have adopted [L. Herrera’s, Phys. Lett. A 165, 206 (1992)] method and static stability criterion of Harisson–Zeldovich–Novikov [B. K. Harrison et al., Gravitational Theory and Gravitational Collapse (University of Chicago Press, 1965); Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics, Vol. 1, Stars and Relativity (University of Chicago Press, 1971)] to analyze the stability of the models.
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DZHUNUSHALIEV, V. "MATCHING CONDITION ON THE EVENT HORIZON AND HOLOGRAPHY PRINCIPLE." International Journal of Modern Physics D 09, no. 05 (2000): 551–60. http://dx.doi.org/10.1142/s0218271800000554.
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It is shown that the event horizon of 4D black hole or ds2=0 surfaces of multidimensional wormhole-like solutions reduce the amount of information necessary for determining the whole spacetime and hence satisfy the Holography principle. This leads to the fact that by matching two metrics on a ds2=0 surface (an event horizon for 4D black holes) we can match only the metric components but not their derivatives. For example, this allows us to obtain a composite wormhole inserting a 5D wormhole-like flux tube between two Reissner–Nordström black holes and matching them on the event horizon. Using the Holography principle, the entropy of a black hole from the algorithm theory is obtained.
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EBERT, D., V. CH ZHUKOVSKY, and A. V. TYUKOV. "DYNAMICAL FERMION MASSES UNDER THE INFLUENCE OF KALUZA–KLEIN FERMIONS AND A BULK ABELIAN GAUGE FIELD." Modern Physics Letters A 25, no. 35 (2010): 2933–45. http://dx.doi.org/10.1142/s0217732310034249.
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The dynamical fermion mass generation on the 3-brane in the 5D spacetime is discussed in a model with bulk fermions in interaction with fermions on the branes assuming the presence of a constant Abelian gauge field A5 in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field A5. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D-fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the fifth dimension is analyzed. The influence of the A5-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the A5 field, the coupling constant and the radius are examined.
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Pereira, Marco. "The Hypergeometrical Universe Theory: Cosmogenesis, Cosmology and Standard Model." World Scientific News 82, no. 1 (2017): 1–96. https://doi.org/10.5281/zenodo.1439076.
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This paper presents a simple and purely geometrical Grand Unification Theory. Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified framework. Newton's Gravitational Law, Gauss' Electrostatics Law and Biot-Savart's Electromagnetism Law are derived from first principles. Gravitational Lensing and Mercury Perihelion Precession are replicated within the theory. Unification symmetry is defined for all the existing forces. This alternative model does not require Strong and Electroweak forces. A 4D Shock-Wave Hyperspherical topology is proposed for the Universe which together with a Quantum Lagrangian Principle and a Dilator based model for matter result in a quantized stepwise expansion for the whole Universe along a radial direction within a 4D spatial manifold. The Hypergeometrical Standard Model for matter, Universe Topology and a new Law of Gravitation are presented. Newton's and Einstein's Laws of Gravitation and Dynamics, Gauss Law of Electrostatics among others are challenged when HU presents Type 1A Supernova Survey results. HU's SN1a results challenge current Cosmological Standard Model (L-CDM) by challenging its Cosmological Ruler d(z). SDSS BOSS dataset is shown to support a new Cosmogenesis theory and HU proposal that we are embedded in a 5D Spacetime. The Big Bang Theory is shown to be challenged by SDSS BOSS dataset. Hyperspherical Acoustic Oscillations are demonstrated in the SDSS BOSS Galaxy density. A New de-Broglie Force is proposed.
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Hieu, Tran Minh, Nguyen Thu Huong, and Trieu Quynh Trang. "Higgs Mass Constraint on a Low Scale SUSY Model." Communications in Physics 26, no. 4 (2017): 369. http://dx.doi.org/10.15625/0868-3166/26/4/9117.
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Randal-Sundrum models have an interesting feature that an effective physical scale can be generated from a much larger one of the underlying theory. In this paper, we investigate a model of supersymmetry in the Randall-Sundrum spacetime with a low cutoff scale. Due to the warp factor, the Kaluza-Klein scale is warped down to \(\mathcal{O}\)(100) TeV. With the MSSM superfields living in the bulk, the soft SUSY breaking terms of the 4D effective theory are derived from the original 5D Lagrangian by integrating out the extra-dimension. We examine the constraint of the Higgs boson mass measurement on the model. As a result, the viable parameter space with the ability to reproduce a 125 GeV Higgs mass is identified. The constraint rules out parameter regions with the stop masses larger than 20 TeV. Therefore, the parameter space of the model can be explored in a future 100 TeV collider.
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PONCE DE LEON, J. "INVARIANT DEFINITION OF REST MASS AND DYNAMICS OF PARTICLES IN 4D FROM BULK GEODESICS IN BRANE-WORLD AND NON-COMPACT KALUZA–KLEIN THEORIES." International Journal of Modern Physics D 12, no. 05 (2003): 757–80. http://dx.doi.org/10.1142/s0218271803003384.
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In the Randall–Sundrum brane-world scenario and other non-compact Kaluza–Klein theories, the motion of test particles is higher-dimensional in nature. In other words, all test particles travel on five-dimensional geodesics but observers, who are bounded to spacetime, have access only to the 4D part of the trajectory. Conventionally, the dynamics of test particles as observed in 4D is discussed on the basis of the splitting of the geodesic equation in 5D. However, this procedure is not unique and therefore leads to some problems. The most serious one is the ambiguity in the definition of rest mass in 4D, which is crucial for the discussion of the dynamics. We propose the Hamilton–Jacobi formalism, instead of the geodesic one, to study the dynamics in 4D. On the basis of this formalism we provide an unambiguous expression for the rest mass and its variation along the motion as observed in 4D. It is independent of the coordinates and any parameterization used along the motion. Moreover, we are able to show a comprehensive picture of the various physical scenarios allowed in 4D, without having to deal with the subtle details of the splitting formalism. Moreover we study the extra non-gravitational forces perceived by an observer in 4D who describes the geodesic motion of a bulk test particle in 5D. Firstly, we show that the so-called fifth force fails to account for the variation of rest mass along the particle's worldline. Secondly, we offer here a new definition that correctly takes into account the change of mass observed in 4D.
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Slagter, Reinoud Jan. "Time evolution of a warped cosmic string." International Journal of Modern Physics D 23, no. 08 (2014): 1450066. http://dx.doi.org/10.1142/s0218271814500667.
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The time evolution of a self-gravitating U(1) cosmic string on a warped five-dimensional (5D) axially symmetric spacetime is numerically investigated. Although cosmic strings are theoretically predicted in four-dimensional (4D) general relativistic models, there is still no observational evidence of their existence. From recent observations of the cosmic microwave background (CMB), it is concluded that these cosmic strings cannot provide a satisfactory explanation for the bulk of density perturbations. They even could not survive inflation. It is conjectured that only in a 5D warped braneworld model there will be observable imprint of these so-called cosmic superstrings on the induced effective 4D brane metric for values of the symmetry breaking scale larger than the grand unified theory (GUT) values. The warp factor makes these strings consistent with the predicted mass per unit length on the brane. However, in a time-dependent setting, it seems that there is a wavelike energy–momentum transfer to infinity on the brane, a high-energy braneworld behavior. This in contrast to earlier results in approximation models. Evidence of this information from the bulk geometry could be found in the gravitational cosmic background radiation via gravitational wave energy–momentum affecting the brane evolution. Fluctuations of the brane when there is a U(1) gauge field present, are comparable with the proposed brane tension fluctuations, or branons, whose relic abundance can be a dark matter candidate. We briefly made a connection with the critical behavior at the threshold of black hole formation found by Choptuik several decades ago in self-gravitating time-dependent scalar field models. The critical distinction between dispersion of the scalar waves and singular behavior fade away when a time-dependent warp factor is present.
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Slagter, Reinoud Jan. "Evidence of cosmic strings by the observation of the alignment of quasar polarization axes on Mpc scale." International Journal of Modern Physics D 27, no. 09 (2018): 1850094. http://dx.doi.org/10.1142/s0218271818500943.
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The recently found alignment of the polarization axes (PA) of quasars in large quasar groups (LQGs) on Mpc scales can be explained by general relativistic cosmic string networks. By considering the cosmic string as a result of spontaneous symmetry breaking of the gauged U(1) abelian Higgs model with topological charge [Formula: see text], many stability features of [Formula: see text]-vortex solutions of superconductivity can be taken over. Decay of the high multiplicity ([Formula: see text]) super-conducting vortex into a lattice of [Formula: see text] vortices of unit magnetic flux is energetically favorable. The temporarily broken axial symmetry will leave an imprint of a preferred azimuthal-angle on the lattice. The stability of the lattice depends critically on the parameters of the model, especially when gravity comes into play. In order to handle the strong nonlinear behavior of the time-dependent coupled field equations of gravity and the scalar-gauge field, we will use a high-frequency approximation scheme to second order on a warped 5D axially symmetric spacetime with the scalar-gauge field residing on the brane. We consider different winding numbers for the subsequent orders of perturbations of the scalar field. A profound contribution to the energy–momentum tensor comes from the bulk spacetime and can be understood as “dark”-energy. The cosmic string becomes super-massive by the contribution of the 5D Weyl tensor on the brane and the stored azimuthal preferences will not fade away. During the recovery to axial symmetry, gravitational and electro-magnetic radiation will be released. The perturbative appearance of a nonzero energy–momentum component [Formula: see text] can be compared with the phenomenon of bifurcation along the Maclaurin–Jacobi sequence of equilibrium ellipsoids of self-gravitating compact objects, signaling the onset of secular instabilities. There is a kind of similarity with the Goldstone-boson modes of spontaneously broken symmetries of continuous groups. The recovery of the SO(2) symmetry from the equatorial eccentricity takes place on a time-scale comparable with the emission of gravitational waves. The emergent azimuthal-angle dependency in our model can be used to explain the aligned PA in LQGs on Mpc scales. Spin axis direction perpendicular to the major axes of LQGs when the richness decreases can be explained as a second-order effect in our approximation scheme by the higher multiplicity terms. The preferred directions are modulo [Formula: see text], with [Formula: see text] being an integer dependent on the [Formula: see text]th order of approximation. When more data of quasars of high redshift becomes available, one could prove that the alignment emerged after the symmetry breaking scale and must have a cosmological origin. The effect of the warp factor on the second-order perturbations could also be an indication of the existence of extra large dimensions.
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Pereira, Marco. "The Case for the Fourth Spatial Dimension and the Hypergeometrical Force." World Scientific News 98 (September 29, 2018): 127–39. https://doi.org/10.5281/zenodo.1439072.
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Here we present evidence of an extra spatial dimension and that our 3D Universe is embedded as a lightspeed expanding hyperspherical hypersurface. Support for this hypothesis comes from (a) SDSS BOSS dataset analysis showing the seeding of Galaxies on the largest scale by spherical acoustic oscillations, (b) the discovery of an Hyperspherical Force, a constraint force that exists only because of the lightspeed hyperspherical expansion. That solves the Spiral Galaxy Rotation Conundrum, (c) the parameterless predictions of all type 1a Supernovae (SN1a) distances from their redshifts z. Lightspeed hyperspherical expansion permits simple short-distance compliance with the Hubble Law.
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Garcia de Andrade, L. C. "Generation of Primordial Magnetic Fields from QED and Higgs-like Domain Walls in Einstein–Cartan Gravity." Universe 8, no. 12 (2022): 658. http://dx.doi.org/10.3390/universe8120658.
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Spacetime torsion is known to be highly suppressed at the end of inflation, which is called preheating. This result was recently shown in (EPJ C (2022)) in the frame of Einstein–Cartan–Brans–Dicke inflation. In this paper, it is shown that a torsionful magnetogenesis in QED effective Lagrangean drives a torsion damping in order to be subsequently amplified by the dynamo effect after the generation of these magnetic fields seeds. This damping on amplification would depend upon the so-called torsion chirality. Here, a cosmic factor gkK is present where K is the contortion vector and k is the wave vector which is connected to the inverse of magnetic coherence length. In a second example, we find Higgs inlationary fields in Einstein–Cartan gravity thick domain walls (DWs). Recently, a modified Einstein–Cartan gravity was given by Shaposhnikov et al. [PRL (2020)] to obtain Higgs-like inflatons as a portal to dark energy. In the case of thick DW, we assume that there is a torsion squared influence, since we are in the early universe where torsion is not so weak as in the late universe as shown by Paul and SenGupta [EPJ C (2019)] in a 5D brane-world. A static DW solution is obtained when the inflationary potential vanishes and Higgs potential is a helical function. Recently, in the absence of inflation, domain wall dynamos were obtained in Einstein–Cartan gravity (EC) where the spins of the nucleons were orthogonal to the wall.