SCALE FACTOR DUALITY WITH MATTER

2011 ◽  
Vol 26 (15) ◽  
pp. 1137-1145 ◽  
Author(s):  
SUNGGEUN LEE
Keyword(s):  
Equation Of State ◽  
Extra Dimensions ◽  
Higher Dimensions ◽  
Scale Factor ◽  
Scalar Tensor Theory ◽  
Duality Transformation ◽  
Four Dimensions ◽  
Tensor Theory ◽  
Six Dimensions

We investigate the scale factor duality of the scalar–tensor theory in four and ten dimensions with matter. It is shown that when the pressure of the matter vanishes (γ = 0 for the equation of state p = γρ), the action is invariant under the duality. In addition, the action is invariant again under the change of the sign of the pressure (p→-p or γ→-γ). In higher dimensions, we distinguish the matter, e.g., in four dimensions px = γxρ and for extra six dimensions py = γy ρ. The scale factor duality in this case is that when γx = 0 the duality transformation acts on the four-dimensional scale factor and the dilaton with the extra dimensions intact while when γy = 0 it acts on the extra six dimensions and the dilaton with four dimensions intact.

SCALAR–TENSOR THEORY IN TEN DIMENSIONS WITH ANISOTROPIC MATTER

2011 ◽  
Vol 26 (01) ◽  
pp. 19-30 ◽  
Author(s):  
SUNGGEUN LEE
Keyword(s):  
Equation Of State ◽  
Three Dimensions ◽  
Anisotropic Fluid ◽  
Scalar Tensor Theory ◽  
Anisotropic Matter ◽  
Scale Factors ◽  
Tensor Theory ◽  
Dimensional Spacetime ◽  
Six Dimensions ◽  
Type Of The Equation

The cosmological behavior is investigated for ten-dimensional scalar–tensor theory with matter. The matter is taken as an anisotropic fluid. As a simple ansatz, the anisotropic fluid for each four and six dimensions satisfies the same type of the equation of state with different coefficients, px,y = γx,yρ. Following the ansatz of the anisotropic matter, the spacetime then has a product structure which means that the spacetime is decomposed as four-dimensional spacetime (Mx) and six-dimensional transverse space (My). We focus on the solution such that the scale factors in each four and six dimensions behave differently. The corresponding cosmological solutions are obtained for general γx,y. By giving specific numeric values for the coefficients of the equation of state γx,y, we find the solution which behaves in such a way that the spatial three dimensions are expanding while the extra six dimensions are contracting.

Is Spacetime Non-metric?

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Mark D. Roberts
Keyword(s):  
General Relativity ◽  
Higher Dimensions ◽  
Christoffel Symbol ◽  
Einstein Frame ◽  
Jordan Frame ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Extra Information ◽  
Tensor Theory ◽  
Palatini Variation

If one assumes higher dimensions and that dimensional reduction from higher dimensions produces scalar-tensor theory and also that Palatini variation is the correct method of varying scalar-tensor theory then spacetime is nonmetric. Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation equations occur are discussed: it is found that the Jordan frame has more information, this can be expressed in several ways, the simplest is that the extra information corresponds to the function multiplying the Ricci scalar in the action. The Einstein frame has the advantages that stress conservation implies no currents and that the field equations are easier to work with. This is illustrated by application to Robertson-Walker spacetime.

scholarly journals Brans - Dicke Cosmology with Causal Viscous Fluid

1996 ◽  
Vol 49 (5) ◽  
pp. 899 ◽  
Author(s):  
N Banerjee ◽  
A Beesham
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Viscous Fluid ◽  
Exact Solutions ◽  
Power Function ◽  
Causal Theory ◽  
Scale Factor ◽  
Scalar Tensor Theory ◽  
Equilibrium Thermodynamics ◽  
Tensor Theory

Exact solutions for the spatially flat (k = 0) Robertson–Walker cosmological model in Brans–Dicke scalar tensor theory have been obtained in the presence of a causal viscous fluid. It is found that if the scale factor is a power function of the scalar field, then solutions can be obtained in the full causal theory but not in the truncated theory of non-equilibrium thermodynamics.

Clifford’s chain and its analogues in relation to the higher polytopes

1972 ◽  
Vol 330 (1583) ◽  
pp. 443-466 ◽  
Keyword(s):  
Infinite Number ◽  
Finite Sequence ◽  
Higher Dimensions ◽  
The Other ◽  
Four Dimensions ◽  
Symmetrical Configuration ◽  
Six Dimensions

Clifford’s chain of theorems on circles in a plane, Grace’s sequence of theorems on spheres, and Grace’s and Brown’s sequence on hyperspheres in four dimensions are unified and completed. This is achieved by demonstrating a correspondence between each configuration and one of Coxeter’s polytopes p gr in space of ( p + g + r + 1) dimensions. Thus Clifford’s configurations of points and circles in a plane correspond to the polytopes 1 1 , r r'. Grace’s figures of points and spheres correspond to polytopes l 2 r ; and Grace’s and Brown’s figures of points and hyperspheres correspond to polytopes l 3 r . As a result it is shown that to Grace’s sequence there may be added two more symmetrical configurations, one of 17280 points and 240 spheres, the other of an infinite number of points and spheres, before the sequence terminates. To Grace’s and Brown’s sequence may be added just one more symmetrical configuration of points and hyperspheres. Furthermore, it is shown that in space either of five or of six dimensions there exists a finite sequence of three configurations; in any space of seven or more dimensions there is a sequence of just two configurations each. A related chain of theorems due to Homersham Cox, more general than Clifford’s, is likewise shown to have analogues in spaces of higher dimensions.

scholarly journals Einstein-Gauss-Bonnet Gravity with Extra Dimensions

Galaxies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 39 ◽  
Author(s):  
Carsten van de Bruck ◽  
Chris Longden
Keyword(s):  
Effective Field Theory ◽  
Modified Gravity ◽  
Extra Dimensions ◽  
Effective Field ◽  
Scalar Tensor Theory ◽  
Gravitational Action ◽  
Matter Coupling ◽  
Tensor Theory ◽  
Spatial Dimensions ◽  
Special Case

We consider a theory of modified gravity possessing d extra spatial dimensions with a maximally symmetric metric and a scale factor, whose ( 4 + d ) -dimensional gravitational action contains terms proportional to quadratic curvature scalars. Constructing the 4D effective field theory by dimensional reduction, we find that a special case of our action where the additional terms appear in the well-known Gauss-Bonnet combination is of special interest as it uniquely produces a Horndeski scalar-tensor theory in the 4D effective action. We further consider the possibility of achieving stabilised extra dimensions in this scenario, as a function of the number and curvature of extra dimensions, as well as the strength of the Gauss-Bonnet coupling. Further questions that remain to be answered such as the influence of matter-coupling are briefly discussed.

scholarly journals The most general second-order field equations of bi-scalar-tensor theory in four dimensions

2015 ◽  
Vol 2015 (7) ◽  
Author(s):  
Seiju Ohashi ◽  
Norihiro Tanahashi ◽  
Tsutomu Kobayashi ◽  
Masahide Yamaguchi
Keyword(s):  
Second Order ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Four Dimensions ◽  
Tensor Theory

scholarly journals Field Independent Cosmic Evolution

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Nayem Sk ◽  
Abhik Kumar Sanyal
Keyword(s):  
Higher Order ◽  
Noether Symmetry ◽  
Scalar Tensor Theory ◽  
Anisotropic Model ◽  
Tachyonic Field ◽  
Tensor Theory ◽  
Cosmic Evolution ◽  
Field Independent ◽  
Conserved Current ◽  
Theory Of Gravity

It has been shown earlier that Noether symmetry does not admit a form of corresponding to an action in which is coupled to scalar-tensor theory of gravity or even for pure theory of gravity taking anisotropic model into account. Here, we prove that theory of gravity does not admit Noether symmetry even if it is coupled to tachyonic field and considering a gauge in addition. To handle such a theory, a general conserved current has been constructed under a condition which decouples higher-order curvature part from the field part. This condition, in principle, solves for the scale-factor independently. Thus, cosmological evolution remains independent of the form of the chosen field, whether it is a scalar or a tachyon.

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