Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on Ġ may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.      

Bulk Viscous Bianchi-III Models with Time Dependent G and?Λ

Bulk Viscous anisotropic Bianchi-III cosmological models are investigated with time dependent gravitational and cosmological constants in the framework of Einstein’s general relativity. In order to get some useful information about the time varying nature of G and Λ, we have assumed an exponentially decaying rest energy density of the universe. The extracted Newtonian gravitational constant G varies with time but its time varying nature depends on bulk viscosity and the anisotropic nature of the model. The cosmological constant Λ is found to decrease with time to a small but positive value for the models.     

Generalized self-similar scalar-tensor theories

In order to analyze how the gravitational constant, G, and the cosmological constant, Λ, may vary we study through symmetry principles the form of the functions in the generalized scalar-tensor theories under the self-similar hypothesis. The results obtained are absolutely general and valid for all the Bianchi models and the flat FRW one. We study the concrete example of the Kantowski–Sachs model finding some new exact self-similar solutions.     

Phenomenological models of Universe with varying G and Λ

In this article we will consider several phenomenological models for the Universe with varying G and Λ(t), where G is the gravitational ”constant” and Λ(t) is a varying cosmological ”constant”. Two-component fluid model are taken into account. An interaction of the phenomenological form between a barotropic fluid and a quintessence DE is supposed. Three different forms of Λ(t) will be considered. The problem is analysed numerically and behavior of different cosmological parameters investigated graphically. Conclusion and discussions are given at the end of the work. In an Appendix information concerning to the other cosmological parameters is presented.     

The $$B\rightarrow \bar{K}\pi \ell \ell $$ distribution at low hadronic recoil

The general class of Bianchi cosmological models with dark energy in the form of modified Chaplygin gas with variable Λ and G and bulk viscosity have been considered. We discuss three types of average scale factor by using a special law for deceleration parameter which is linear in time with negative slope. The exact solutions to the corresponding field equations are obtained. We obtain the solution of bulk viscosity (ξ), cosmological constant (Λ), gravitational parameter (G) and deceleration parameter (q) for different equations of state. The model describes an accelerating Universe for large value of time t, wherein the effective negative pressure induced by Chaplygin gas and bulk viscous pressure are driving the acceleration.     

On gravitational shock waves in curved spacetimes

Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and a cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the d-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström and the d-dimensional Schwarzschild solution as subcases), the 4-dimensional De Sitter and anti-De Sitter spaces (and the Schwarzschild-De Sitter black hole), the 3-dimensional anti-De Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string-inspired gravitational solutions nd give a few examples.     

TCP, quantum gravity,the cosmological constant and all that...

We study cosmology from the point of view of quantum gravity. Some light is thrown on the nature of time, and it is suggested that the cosmological arrow of time is generated by a spontaneous breakdown of TCP. Conventional cosmological models in which quantum fields interact with a time-dependent gravitational field are shown to describe an approximation to the quantum gravitational wave function which is valid in the long-wavelength limit. Two problems with initial conditions are resolved in models in which a negative bare cosmological constant is cancelled by the classical excitation of a Bose field η with a very flat potential. These models can also give a natural explanation for the observed value of the cosmological constant.     

Bianchi I in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.     

Higher Dimensional Unified Description of Early Universe with Variable <Emphasis Type="Italic">G</Emphasis> and Λ

A homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with varying gravitational and cosmological constant is studied in the context of higher dimensional space time. Exact solution of the field equations are obtained by using the “gamma law” equation of state p=(γ−1)ρ, where γ is adiabatic parameter varies continuously as the universe expands. The functional form γ which is assumed to be the function of scale factor R as proposed by Carvalho (1996) is used to analyse the behavior of scale factor R, cosmological constant Λ and the gravitational constant G for two different phases: inflation and radiation. The various physical aspects of the early cosmological models has also been discussed in the framework of higher dimensional space time.     

Two-Fluid Anisotropic Cosmological Model with Variable G and Λ

Two-fluid anisotropic Bianchi type-III cosmological model is investigated with variable gravitational constant G and cosmological constant Λ in the framework of Einstein’s general relativity. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the cosmic microwave background radiation. The dynamics of the anisotropic universe with variable G and Λ are discussed. We also discussed in detail the behavior of associated fluid parameters and kinematical parameters.     

A note on the generalized Friedmann equations for a thick brane

Within our thick brane approach previously used to obtain the cosmological evolution equations on a thick brane embedded in a five-dimensional Schwarzschild Anti-de Sitter spacetime it is explicitly shown that the consistency of these equations with the energy conservation equation requires that, in general, the thickness of the brane evolves in time. This varying brane thickness entails the possibility that both Newton’s gravitational constant G and the effective cosmological constant Λ₄ are time dependent.     

<Emphasis Type="Italic">C</Emphasis>-field Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in FRW Space–Time

C-field cosmological models based on Hoyle-Narlikar theory with variable gravitational constant G in the frame work of FRW (Friedmann-Robertson-Walker) space–time for positive and negative curvatures are investigated. To get the deterministic solutions in terms of cosmic time t, we have assumed G=R ⁿ and discussed for n=−1, −2, R being scalar factor. In both the cases, creation field C increases with time, the gravitational constant G and matter density (ρ) decrease with time in the model (21). In the model (41) G decreases with time and matter density (ρ) is constant. The other physical aspects of the models are also discussed.     

Amplification of Gravitational Waves in Scalar-Tensor Inflationary Lambda-Model

After reviewing the scalar-tensor inflationary solutions by Berman and Trevisan (Int. J. Theor. Phys. 29, 1411–1414, 2009), we obtain solutions for the amplification of gravitational waves in the models. The solutions consider a perfect gas equation of state, with cosmic pressure proportional to the energy density, the proportionality constant being smaller than −2/3, and a cosmological term.     

Dynamical dimensional reduction

We propose to call a dynamical dimensional reduction effective if the corresponding dynamical system possesses a single attracting critical point representing expanding physical space-time and static internal space. We show that theBV × T ^D multidimensional cosmological model with a hydrodynamic energy-momentum tensor provides an example of effective dimensional reduction. We also study the dynamics of the multidimensional cosmological model of typeBI × T ^D with an energy-momentum tensor representing low temperature quantum effects, monopole contribution and the cosmological constant. It turns out that anisotropy and the cosmological constant are crucial for the process of dimensional reduction to be effective. We argue that this is the general property of homogeneous multidimensional cosmological models.     

Localization of Gravity in Brane World with Arbitrary Extra Dimensions

We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. We used the confining potential in this model to localized gravitons on the brane. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.     

Cosmological compactification in Kaluza-Klein model and time-dependent cosmological term

Einstein's equations for the generalized (4+D)-dimensional Robertson-Walker model are solved taking the conformally invariant action for the matter field. Compactification of this model is discussed and the compactification time/compactification mass scale for different values ofD is calculated. The resulting 4-dimensional action for gravity is obtained. It is found that a time-dependent cosmological constant is induced which is very large when the cosmic time is small and very small when the cosmic time is large.     

Cosmological application on five-dimensional teleparallel theory equivalent to general relativity

A theory of(4+1)-dimensional gravity has been developed on the basis of which equivalent to the theory of general relativity by teleparallel.The fundamental gravitational field variables are the 5-dimensional(5D) vector fields(pentad),defined globally on a manifold M,and gravity is attributed to the torsion.The Lagrangian density is quadratic in the torsion tensor.We then apply the field equations to two different homogenous and isotropic geometric structures which give the same line element,i.e.,FRW in five dimensions.The cosmological parameters are calculated and some cosmological problems are discussed.     

Holographic Dark Energy in Higher Derivative Gravity with Varying Gravitational Constant

In this paper we investigate the holographic dark energy scenario in higher derivative gravity with a varying gravitational constant. We introduce a kind of energy density from higher derivative gravity which has role of the same as holographic dark energy. We obtain the exact differential equation , which determine the evolution of the dark energy density based on varying gravitational constant G. We also find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for low redshifts containing varying G correction.     

Hierarchy problem and the cosmological constant in a five-dimensional Brans-Dicke brane world model

We discuss a new solution, admitting the existence of dS ₄ branes, in five-dimensional Brans-Dicke theory. It is shown that, due to a special form of a bulk scalar field potential, for certain values of the model parameters the effective cosmological constant can be made small on the brane, where the hierarchy problem of gravitational interaction is solved. We also discuss new stabilization mechanism which is based on the use of auxiliary fields.