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Register a new userGravitational excitons from extra dimensions
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Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces near minima of an effective potential have a form of massive scalar fields in the external space-time. Parameters of models which ensure minima of the effective potentials are obtained for particular cases and masses of gravitational excitons are estimated.
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Considering a n-dimensional general spacetime, we deduce its 4-dimensional Einstein equation and Friedman equations, and discover a general dual relation between the scale factor $a(t)$ of our universe and the scale factor $B(t)$ of extra dimensions. Based on the dual relation equation, predictions of shrinking of extra dimensions and free of singularity problem of our universe are given. Therefore, solution to initial singularity paradox of our universe is achieved. Because the dual relation is general, this Letter discovers that it is just the extra dimensional shrinking contribution that results in our universes expanding in terms of the dual relation in the bulk space, and actually the dual relation is deduced doesnt depend on the 4-dimensional matter concrete Lagrangian, these are key important for a lot of future relative investigations.
This paper provides a pedagogical introduction to the physics of extra dimensions focussing on the ADD, Randall-Sundrum and DGP models. In each of these models, the familiar particles and fields of the standard model are assumed to be confined to a four dimensional space-time called the brane; the brane is a slice through a higher dimensional space-time called the bulk. The geometry of the ADD, Randall-Sundrum and DGP space-times is described and the relation between Randall-Sundrum and Anti-de-Sitter space-time is explained. The necessary differential geometry background is introduced in an appendix that presumes no greater mathematical preparation than multivariable calculus. The ordinary wave equation and the Klein-Gordon equation are briefly reviewed followed by an analysis of the propagation of scalar waves in the bulk in all three extra-dimensional models. We also calculate the scalar field produced by a static point source located on the brane for all three models. For the ADD and Randall-Sundrum models at large distances the field looks like that of a point source in four space-time dimensions but at short distances it crosses over to a form appropriate to the higher dimensional space-time. For the DGP model the field has the higher dimensional form at long distances rather than short. The scalar field results provide qualitative insights into the corresponding behavior of gravitational fields. In particular the explanation within the ADD and Randall-Sundrum model of the weakness of gravity compared to other forces is discussed as are the implications of the two models for colliders and other experiments.
We develop a Hamiltonian formalism of brane-world gravity, which singles out two preferred, mutually orthogonal directions. One is a unit twist-free field of spatial vectors with integral lines intersecting perpendicularly the brane. The other is a temporal vector field with respect to which we perform the Arnowitt-Deser-Misner decomposition of the Einstein-Hilbert Lagrangian. The gravitational variables arise from the projections of the spatial metric and their canonically conjugated momenta as tensorial, vectorial and scalar quantities defined on the family of hypersurfaces containing the brane. They represent the gravitons, a gravi-photon and a gravi-scalar, respectively. From the action we derive the canonical evolution equations and the constraints for these gravitational degrees of freedom both on the brane and outside it. By integrating across the brane, the dynamics also generates the tensorial and scalar projection of the Lanczos equation. The vectorial projection of the Lanczos equation arises in a similar way from the diffeomorphism constraint. Both the graviton and the gravi-scalar are continuous across the brane, however the momentum of the gravi-vector has a jump, related to the energy transport (heat flow) on the brane.
In 6D general relativity with a phantom scalar field as a source of gravity, we present solutions that implement a transition from an effective 4D geometry times small extra dimensions to an effectively 6D space-time where the physical laws are different from ours. We consider manifolds with the structure M0 x M1 x M2, where M0 is 2D Lorentzian space-time while each of M1 and M2 can be a 2-sphere or a 2-torus. Some solutions describe wormholes with spherical symmetry in our space-time and toroidal extra dimensions. Others are of black universe type: at one end there is a 6D asymptotically anti-de Sitter black hole while beyond the horizon the geometry tends to a 4D de Sitter cosmology times a small 2D spherical extra space.
We demonstrate a new model which uses an ADD type braneworld scenario to produce a multi-state theory of dark matter. Compactification of the extra dimensions onto a sphere leads to the association of a single complex scalar in the bulk with multiple Kaluza-Klein towers in an effective four-dimensional theory. A mutually interacting multi-state theory of dark matter arises naturally within which the dark matter states are identified with the lightest Kaluza-Klein particles of fixed magnetic quantum number. These states are protected from decay by a combination of a global U(1) symmetry and the continuous rotational symmetry about the polar axis of the spherical geometry. We briefly discuss the relic abundance calculation and investigate the spin-independent elastic scattering off nucleons of the lightest and next-to-lightest dark matter states.
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