Abstract
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 the equality between two radii B=C, which permits us to solve exactly the equations of motion. One relation between the scale factors (A,C) via the solutions is found. With this hidden symmetry, then we solve the FRW model, 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, building a wavepacket when the scalar fields have a hyperbolic behavior, obtaining some qualitative results when we analyze the projection plane to the wall formed by the probability density. Bohm’s formalism for this cosmological model is revisited too.
Highlights
One of the most important things that we have learned from Planck’s results [1] is related to the little anisotropies of the universe
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
We have found from the fields equations (8a), (8b), and (8c) that radii B and C are equal for the Bianchi VIh=−1, this classical hidden symmetry is relevant in the quantum level, because, 21 years ago, a generic quantum solution was found for all Bianchi Class A cosmological models in Bohm’s formalism [21], and in particular for the Bianchi type VIh=−1 it was necessary to modify the general structure of the generic solution with a function over the coordinate β1 − β2; with this result, the modification is not necessary, due to the fact that this function is a constant as we see using Misner’s parameterization of this cosmological model
Summary
One of the most important things that we have learned from Planck’s results [1] is related to the little anisotropies of the universe.
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