scholarly journals HIGHER DIMENSIONAL DUST COSMOLOGICAL IMPLICATIONS OF A DECAY LAW FOR THE Λ TERM: EXPRESSIONS FOR SOME OBSERVABLE QUANTITIES

2006 ◽  
Vol 15 (01) ◽  
pp. 95-105 ◽  
Author(s):  
G. S. KHADEKAR ◽  
ANIRUDH PRADHAN ◽  
M. R. MOLAEI
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Nucl Phys ◽  
De Sitter ◽  
Angular Diameter Distance ◽  
Proper Distance ◽  
Higher Dimensional ◽  
Significant Difference ◽  
Dimensional Space Time ◽  
Sitter Model

We have considered the multidimensional cosmological implications of a decay law for the Λ term that is proportional to [Formula: see text], where β is a constant and a is the scale factor of RW-space–time. We discuss the cosmological consequences of a model for the vanishing pressure for the case k = 0. It has been observed that such models are compatible with the result of recent observations and the cosmological term Λ gradually reduces as the universe expands. In this model, Λ varies as the inverse square of time, which matches its natural units. The proper distance, the luminosity distance-redshift, the angular diameter distance-redshift, and look back time-redshift for the model are presented in the framework of higher dimensional space–time. The model of the Freese et al. (Nucl. Phys. B287, 797 (1987)) for n = 2 is retrieved for the particular choice of A0and also the Einstein–de Sitter model is obtained for [Formula: see text]. This work has thus generalized to higher dimensions the well-known result in four-dimensional space–time. It is found that there may be a significant difference, in principle at least, to the analogous situation in four-dimensional space–time.

scholarly journals THE WARPING OF EXTRA SPACES ACCELERATES THE EXPANSION OF THE UNIVERSE

2010 ◽  
Vol 19 (14) ◽  
pp. 2281-2287 ◽  
Author(s):  
ISHWAREE P. NEUPANE
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
De Sitter ◽  
Four Dimensions ◽  
Accelerating Expansion ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Expansion Of The Universe ◽  
Theories Of Gravity ◽  
The Universe

Generic cosmological models derived from higher-dimensional theories with warped extra-dimensions have a nonzero cosmological constant-like term induced on the 3 + 1 space–time, or a physical three-brane. In the scenario where this 3 + 1 space–time is an inflating de Sitter "bran" embedded in a higher-dimensional space–time, described by warped geometry, the four-dimensional cosmological term is determined in terms of two length scales: one is a scale associated with the size of extra-dimension(s) and the other is a scale associated with the warping of extra-space(s). The existence of this term in four dimensions provides a tantalizing possibility of explaining the observed accelerating expansion of the universe from fundamental theories of gravity, e.g. string theory.

scholarly journals Kaluza–Klein reduction and Bergmann–Wagoner bi-scalar general action of scalar–tensor gravity

2015 ◽  
Vol 12 (10) ◽  
pp. 1550106 ◽  
Author(s):  
Kazuharu Bamba ◽  
Davood Momeni ◽  
Ratbay Myrzakulov
Keyword(s):  
Dimensional Reduction ◽  
Dimensional Space ◽  
Space Time ◽  
De Sitter ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
General Action ◽  
The Stability ◽  
Kaluza Klein

We examine the Kaluza–Klein (KK) dimensional reduction from higher dimensional space-time and the properties of the resultant Bergmann–Wagoner general action of scalar–tensor theories. With the analysis of the perturbations, we also investigate the stability of the anti-de Sitter (AdS) space-time in the (D ∈ 𝒩)-dimensional Einstein gravity with the negative cosmological constant. Furthermore, we derive the conditions for the dimensional reduction to successfully be executed and present the KK compactification mechanism.

scholarly journals Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3

2017 ◽  
Vol 3 ◽  
pp. e123 ◽  
Author(s):  
Ken Arroyo Ohori ◽  
Hugo Ledoux ◽  
Jantien Stoter
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Three Dimensions ◽  
Time And Space ◽  
3D Objects ◽  
Levels Of Detail ◽  
Higher Dimensional Space Time ◽  
Space Scale ◽  
Higher Dimensional ◽  
Dimensional Space Time

Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object’s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from ℝ4to ℝ3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple ‘long axis’ projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (S3) followed by a stereographic projection to ℝ3, which results in an inwards-outwards fourth axis. Our focus is in using these projections from ℝ4to ℝ3, but they are formulated from ℝnto ℝn−1so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.

scholarly journals First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 783 ◽  
Author(s):  
Shumaila Javeed ◽  
Sidra Riaz ◽  
Khurram Saleem Alimgeer ◽  
M. Atif ◽  
Atif Hanif ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Dimensional Space ◽  
Nonlinear Partial Differential Equations ◽  
First Integral ◽  
Mathematical Physics ◽  
Space Time ◽  
Mathematical Tool ◽  
Long Wave ◽  
Higher Dimensional ◽  
Dimensional Space Time

In this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.

scholarly journals Gravitational Theory Without the Cosmological Constant Problem

1997 ◽  
Vol 12 (32) ◽  
pp. 2421-2424 ◽  
Author(s):  
E. I. Guendelman ◽  
A. B. Kaganovich
Keyword(s):  
Cosmological Constant ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Realistic Model ◽  
Gravitational Theory ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time

We develop a gravitational theory where the measure of integration in the action principle is not necessarily [Formula: see text] but it is determined dynamically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of "non-gravitating vacuum energy" which states that the Lagrangian density L can be changed to L + const. without affecting the dynamics. Formulating the theory in the first-order formalism we get as a consequence of the variational principle a constraint that enforces the vanishing of the cosmological constant. The most realistic model that implements these ideas is realized in a six or higher dimensional space–time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that the remaining four-dimensional space–time must have effective zero cosmological constant.

scholarly journals Space–times over normed division algebras, revisited

2020 ◽  
Vol 35 (10) ◽  
pp. 2050055
Author(s):  
R. Vilela Mendes
Keyword(s):  
Homogeneous Spaces ◽  
Dimensional Space ◽  
Internal Symmetry ◽  
Space Time ◽  
Mathematical Framework ◽  
The Real ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Symmetry Transformations ◽  
Extended Group

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the Standard Model and grand unified theories. Less discussed has been the question of why such algebraic structures appear in Nature. One possibility could be an intrinsic complex, quaternionic or octonionic nature of the space–time manifold. Then, an obvious question is why space–time appears nevertheless to be simply parametrized by the real numbers. How the real slices of an higher-dimensional space–time manifold might be almost independent from each other is discussed here. This comes about as a result of the different nature of the representations of the real kinematical groups and those of the extended spaces. Some of the internal symmetry transformations might however appear as representations on homogeneous spaces of the extended group transformations that cannot be implemented on the elementary states.

scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

Sign in / Sign up

Export Citation Format

Share Document