scholarly journals The Quest for a Realistic Four-dimensional Cosmology

2011 ◽  
Vol 1 ◽  
pp. 18-24
Author(s):  
Ishwaree P Neupane
Keyword(s):  
Cosmological Constant ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
De Sitter ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Gravitational Vacuum ◽  
Theories Of Gravity ◽  
The Universe ◽  
Kaluza Klein

The existence of a small and positive cosmological constant attributed to gravitational vacuum energy (or dark energy) in the present-day universe appears to be the most pressing obstacle as well as opportunity to significantly improving the models of four-dimensional cosmology from fundamental theories of gravity, including string theory and modern Kaluza-Klein theories. In seeking to resolve this problem, one naturally wonders if the real world can somehow be interpreted as an inflating de Sitter "brane" embedded in a five or even higher-dimensional space-time described by warped or non-factorizable geometry. In this scenario, the four-dimensional cosmological constant may well be determined in terms of two length scales: one is a scale associated with the size of extra dimensions and the other is a scale associated with the expansion rate of the universe, which is also related to the warping of extra spaces.Key words: CosmologyThe Himalayan Physics Vol.1, No.1, May, 2010Page: 18-24Uploaded Date: 28 July, 2011

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.

HIGHER DIMENSIONAL SPACE–TIME MODEL FOR A DUST-FILLED UNIVERSE WITH A COSMOLOGICAL CONSTANT

2003 ◽  
Vol 12 (05) ◽  
pp. 905-911 ◽  
Author(s):  
NABAJIT CHAKRAVARTY ◽  
BATUL CHANDRA SANTRA ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Cosmological Constant ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Matter Field ◽  
Vacuum Energy Density ◽  
Time Model ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Space Time Model ◽  
The Universe

In recent years it is generally believed that we should consider positive vacuum energy density or cosmological constant. Also as higher dimensional theory is important at the early stages of the Universe, so it will be interesting to study classical tests of cosmology in a higher dimensional generalized Kantowski–Sachs model. For matter field, we consider dust and a cosmological constant and examine which are physically permissible.

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 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.

BLACK HOLE QUANTIZATION, THERMODYNAMICS AND COSMOLOGICAL CONSTANT

2004 ◽  
Vol 13 (05) ◽  
pp. 885-898
Author(s):  
LI XIANG
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Planck Scale ◽  
Additional Term ◽  
Logarithmic Correction ◽  
De Sitter ◽  
Horizon Area ◽  
Constant Distance ◽  
The Universe

Bekenstein argues that the horizon area of a black hole has a constant distance spectrum. We investigate the effects of such a discrete spectrum on the thermodynamics of a Schwarzchild black hole (SBH) and a Schwarzchild–de Sitter black hole (SdBH), in terms of the time-energy uncertainty relation and Stefan–Boltzman law. For the massive SBH, a negative and logarithmic correction to the Bekenstein–Hawking entropy is obtained, as well as other authors by using other methods. As to the minimal hole near the Planck scale, its entropy is no longer proportional to the horizon area, but is of order of the mass of the hole. This is similar to an excited stringy state. The vanishing heat capacity of such a minimal black hole implies that it may be a remnant as the ground state of the evaporating hole. The properties of a SdBH are similar to the SBH, except for an additional term of square area associated with the cosmological constant. In order to maintain the validity of the Bekenstein–Hawking formula, the cosmological constant is strongly limited by the size of the biggest black hole in the universe. A relation associated with the cosmological constant, Planck area and the Stefan–Boltzman constant is obtained. The cosmological constant is not only related to the vacuum energy, but is also related to the thermodynamics.

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.

Conformal evolution of phantom dominated final stages of the universe in higher dimensions

2020 ◽  
pp. 1-9 ◽  
Author(s):  
S. Natarajan ◽  
R. Chandramohan
Keyword(s):  
Loop Quantum Gravity ◽  
Dimensional Space ◽  
Friedmann Equation ◽  
Higher Dimensions ◽  
Higher Dimensional ◽  
Loop Quantization ◽  
The Universe ◽  
Modified Equation ◽  
Work Loop ◽  
Kaluza Klein

Friedmann solutions and higher-dimensional 5D Kaluza–Klein solutions using mathematical packages such as Sagemath and Cadabra are calculated. A modified Friedmann equation powered by loop quantum gravity in higher dimensions is calculated in this work. Loop quantization in extra-dimensional space is predicted. Modified equation of state for non-interacting dark matter and dark energy are calculated. It has been predicted that the higher curvature due to phantom density would be a local kind of quantized curvature. The modified Friedmann solutions with Kaluza–Klein interpretation are found. To achieve a conformal exit, the non-interacting solutions are discussed in this work. The obtained results are compared with the ΛCDM and quintessence models. The results support conformal cyclic cosmology, which predicts the conformal evolution of the universe without facing any singularity as the result of topological effects.

scholarly journals ON KALUZA–KLEIN SPACE–TIME IN EINSTEIN–GAUSS–BONNET GRAVITY

2009 ◽  
Vol 18 (04) ◽  
pp. 599-611 ◽  
Author(s):  
ALFRED MOLINA ◽  
NARESH DADHICH
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Dimensional Space ◽  
Space Time ◽  
Two Dimensional ◽  
Bonnet Gravity ◽  
Space Of Constant Curvature ◽  
Dimensional Black Hole ◽  
Dimensional Space Time ◽  
Kaluza Klein

By considering the product of the usual four-dimensional space–time with two dimensional space of constant curvature, an interesting black hole solution has recently been found for Einstein–Gauss–Bonnet gravity. It turns out that this as well as all others could easily be made to radiate Vaidya null dust. However, there exists no Kerr analog in this setting. To get the physical feel of the four-dimensional black hole space–times, we study asymptotic behavior of stresses at the two ends, r → 0 and r → ∞.

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.

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