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Register a new userCompact Hyperbolic Extra Dimensions: Branes, Kaluza-Klein Modes and Cosmology
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We reconsider theories with low gravitational (or string) scale M_* where Newtons constant is generated via new large-volume spatial dimensions, while Standard Model states are localized to a 3-brane. Utilizing compact hyperbolic manifolds (CHMs) we show that the spectrum of Kaluza-Klein (KK) modes is radically altered. This allows an early universe cosmology with normal evolution up to substantial temperatures, and completely negates the constraints on M_* arising from astrophysics. Furthermore, an exponential hierarchy between the usual Planck scale and the true fundamental scale of physics can emerge with only order unity coefficients. The linear size of the internal space remains small. The proposal has striking testable signatures.
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We discuss the Kaluza-Klein reduction of spaces with (anti-)self-dual Weyl tensor and point out the emergence of the Einstein-Weyl equations for the reduction from four to three dimensions. As a byproduct we get a simple expression for the gravitational instanton density in terms of the Kaluza-Klein functions.
We investigate the Kaluza-Klein braneworld cosmology from the point of view of observers on the brane. We first generalize the Shiromizu-Maeda-Sasaki (SMS) equations to higher dimensions. As an application, we study a (4+n)-dimensional brane with n dimensions compactified on the brane, in a (5+n)-dimensional bulk. By assuming that the size of the internal space is static, that the bulk energy-momentum tensor can be neglected, we determine the effect of the bulk geometry on the Kaluza-Klein braneworld. Then we derive the effective Friedmann equation on the brane. It turns out that the Friedmann equation explicitly depends on the equation of state, in contrast to the braneworld in a 5-dimensional bulk spacetime. In particular, in a radiation-dominated era, the effective Newton constant depends on the scale factor logarithmically. If we include a pressureless matter on the brane, this dependence disappears after the radiation-matter equality. This may be interpreted as stabilization of the Newton constant by the matter on the brane. Our findings imply that the Kaluza-Klein braneworld cosmology is quite different from the conventional Kaluza-Klein cosmology even at low energy.
We address the issue of radiative corrections to Kaluza-Klein (KK) masses in five-dimensional QED supplemented by aether Lorentz-violating terms. Specifically, we compute the corrections to the KK photon masses from one fermion loop. In general, the KK masses receive radiative corrections due to breaking the five-dimensional Lorentz invariance by compactification. As we show, the presence of the additional Lorentz violating factor - an aether background, leads to the non-trivial modification of these corrections. This model may be of interest in addressing important phenomenological issues such as the relation between radiative corrected KK mass splitting of a particular mode and uncertainties in the measurements and/or possible spatial variation of the fine-structure constant. For the recent data on the fine-structure constant, we find a KK mass splitting of magnitude $sim 0.01$ MeV for the first excited Kaluza-Klein gauge boson at TeV scale. On the other hand, the large KK modes limit displays a very interesting phenomenon, showing the very special role of the aether in protecting the higher modes from the quantum corrections.
We investigate five-dimensional vacuum solutions which represent rotating multi-black holes in asymptotically Kaluza-Klein spacetimes. We show that multi-black holes rotate maximally along extra dimension, and stationary configurations in vacuum are achieved by the balance of the gravitational attraction force and repulsive force caused by the rotations of black holes. We also show that each black hole can have the different topology of the lens space in addition to the spherical topology, and mass of black holes are quantized by the size of extra dimension and horizon topology.
A recently proposed mechanism for large-scale structure in string cosmology --based on massless axionic seeds-- is further analyzed and extended to the acoustic-peak region. Existence, structure, and normalization of the peaks turn out to depend crucially on the overall evolution of extra dimensions during the pre-big bang phase: conversely, precise cosmic microwave background anisotropy data in the acoustic-peak region will provide, within the next decade, a window on string-theorys extra dimensions before their eventual compactification.
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