Time-dependent toroidal compactification proposals and the Bianchi type I model: classical and quantum solutions

In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. This approach is applied to anisotropic cosmological Bianchi type I model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Under this approach, we present an isotropization mechanism for the Bianchi I cosmological model through the analysis of the ratio between the anisotropic parameters and the volume of the Universe which in general keeps constant or runs into zero for late times. We also find that the presence of extra dimensions in this model can accelerate the isotropization process depending on the momenta moduli values. Finally, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology.Comment: LaTeX source, 16 pages, Modified title and additional references. Advances in High Energy Physics, 201

Classical solutions in five dimensional induced matter theory and its relation to an imperfect fluid

We study five dimensional cosmological models with four dimensional hypersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter equations $\rm G_{\mu\nu}=T_{\mu\nu}$ and the matter is interpreted as a purely geometrical property of a fifth dimension. Also, we find that the energy-momentum tensor induced from the fifth dimension has the structure of an imperfect fluid that has dissipative terms.Comment: 16 pages, latex, no figure

Classical Bianchi type I cosmology in K-essence theory

We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid modeling the usual matter content and with cosmological constant. The classical solutions for any but the stiff fluid and without cosmological constant are found in closed form, using a time transformation. We also present the solution whith cosmological constant and some particular values of the barotropic parameter. We present the possible isotropization of the cosmological model, using the ratio between the anisotropic parameters and the volume of the universe and show that this tend to a constant or to zero for different cases. We include also a qualitative analysis of the analog of the Friedmann equation.Comment: 15 pages with one figure, accepted in Advances in High Energy Physic

Cosmological Bianchi Class A models in S\'aez-Ballester theory

We use the S\'aez-Ballester (SB) theory on anisotropic Bianchi Class A cosmological model, with barotropic fluid and cosmological constant, using the Hamilton or Hamilton-Jacobi approach. Contrary to claims in the specialized literature, it is shown that the S\'aez-Ballester theory cannot provide a realistic solution to the dark matter problem of Cosmology for the dust epoch, without a fine tunning because the contribution of the scalar field in this theory is equivalent to a stiff fluid (as can be seen from the energy--momentum tensor for the scalar field), that evolves in a different way as the dust component. To have similar contributions of the scalar component and the dust component implies that their past values were fine tunned. So, we reinterpreting this null result as an indication that dark matter plays a central role in the formation of structures and galaxy evolution, having measureable effects in the cosmic microwave bound radiation, and than this formalism yield to this epoch as primigenius results. We do the mention that this formalism was used recently in the so called K-essence theory applied to dark energy problem, in place to the dark matter problem. Also, we include a quantization procedure of the theory which can be simplified by reinterpreting the theory in the Einstein frame, where the scalar field can be interpreted as part of the matter content of the theory, and exact solutions to the Wheeler-DeWitt equation are found, employing the Bianchi Class A cosmological models.Comment: 24 pages; ISBN: 978-953-307-626-3, InTec

Cosmologies with scalar fields from higher dimensions applied to Bianchi type VIh=−1\rm VI_{h=-1} model: classical and quantum solutions

In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. The corresponding action in four dimensions is similar to the action of K-essence theories. This approach is applied to anisotropic cosmological Bianchi type $VI_{(h=-1)}$ model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. The classical Einstein field equations give us a hidden symmetry, corresponding to equal radii B=C, which permits us to solve exactly the equations of motion. With this hidden symmetry, then we solve the FRW, finding that the scale factor goes to B radii. Also the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology is solved. Bohm's formalism for this cosmological model is revisited too.Comment: 13 pages, 1 figur