Sculpting the Extra Dimensions: Inflation from Codimension-2 Brane Back-reaction

We construct an inflationary model in 6D supergravity that is based on explicit time-dependent solutions to the full higher-dimensional field equations, back-reacting to the presence of a 4D inflaton rolling on a space-filling codimension-2 source brane. Fluxes in the bulk stabilize all moduli except the `breathing' modulus (that is generically present in higher-dimensional supergravities). Back-reaction to the inflaton roll causes the 4D Einstein-frame on-brane geometry to expand, a(t) ~ t^p, as well as exciting the breathing mode and causing the two off-brane dimensions to expand, r(t) ~ t^q. The model evades the general no-go theorems precluding 4D de Sitter solutions, since adjustments to the brane-localized inflaton potential allow the power p to be dialed to be arbitrarily large, with the 4D geometry becoming de Sitter in the limit p -> infinity (in which case q = 0). Slow-roll solutions give accelerated expansion with p large but finite, and q = 1/2. Because the extra dimensions expand during inflation, the present-day 6D gravity scale can be much smaller than it was when primordial fluctuations were generated - potentially allowing TeV gravity now to be consistent with the much higher gravity scale required at horizon-exit for observable primordial gravity waves. Because p >> q, the 4 on-brane dimensions expand more quickly than the 2 off-brane ones, providing a framework for understanding why the observed four dimensions are presently so much larger than the internal two. If uplifted to a 10D framework with 4 dimensions stabilized, the 6D evolution described here could describe how two of the six extra dimensions evolve to become much larger than the others, as a consequence of the enormous expansion of the 4 large dimensions we can see.Comment: 27 pages + appendices, 2 figure

Bulk Axions, Brane Back-reaction and Fluxes

Extra-dimensional models can involve bulk pseudo-Goldstone bosons (pGBs) whose shift symmetry is explicitly broken only by physics localized on branes. Reliable calculation of their low-energy potential is often difficult because it requires details of the stabilization of the extra dimensions. In rugby ball solutions, for which two compact extra dimensions are stabilized in the presence of only positive-tension brane sources, the effects of brane back-reaction can be computed explicitly. This allows the calculation of the shape of the low-energy pGB potential and response of the extra dimensional geometry as a function of the perturbing brane properties. If the pGB-dependence is a small part of the total brane tension a very general analysis is possible, permitting an exploration of how the system responds to frustration when the two branes disagree on what the proper scalar vacuum should be. We show how the low-energy potential is given by the sum of brane tensions (in agreement with common lore) when only the brane tensions couple to the pGB. We also show how a direct brane coupling to the flux stabilizing the extra dimensions corrects this result in a way that does not simply amount to the contribution of the flux to the brane tensions. We calculate the mass of the would-be zero mode, and briefly describe several potential applications, including a brane realization of `natural inflation,' and a dynamical mechanism for suppressing the couplings of the pGB to matter localized on the branes. Since the scalar can be light enough to be relevant to precision tests of gravity (in a technically natural way) this mechanism can be relevant to evading phenomenological bounds.Comment: 36 pages, JHEP styl

Comment on Higgs Inflation and Naturalness

We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.Comment: 5 pages, 1 figure V3: Journal Versio

Quantum fields in disequilibrium: neutral scalar bosons with long-range, inhomogeneous perturbations

Using Schwinger's quantum action principle, dispersion relations are obtained for neutral scalar mesons interacting with bi-local sources. These relations are used as the basis of a method for representing the effect of interactions in the Gaussian approximation to field theory, and it is argued that a marked inhomogeneity, in space-time dependence of the sources, forces a discrete spectrum on the field. The development of such a system is characterized by features commonly associated with chaos and self-organization (localization by domain or cell formation). The Green functions play the role of an iterative map in phase space. Stable systems reside at the fixed points of the map. The present work can be applied to self-interacting theories by choosing suitable properties for the sources. Rapid transport leads to a second order phase transition and anomalous dispersion. Finally, it is shown that there is a compact representation of the non-equilibrium dynamics in terms of generalized chemical potentials, or equivalently as a pseudo-gauge theory, with an imaginary charge. This analogy shows, more clearly, how dissipation and entropy production are related to the source picture and transform a flip-flop like behaviour between two reservoirs into the Landau problem in a constant `magnetic field'. A summary of conventions and formalism is provided as a basis for future work.Comment: 23 pages revte

LP (a) levels and apo (a) phenotypes in urban black South African men

CITATION: Carstens, M. E., Burgess, L. J. & Taljaard, J. J. F. 1998. LP (a) levels and apo (a) phenotypes in urban black South African men. South African Medical Journal, 88:139-142.The original publication is available at http://www.samj.org.zaObjective. To investigate the lipoprotein (a) (Lp (a)) levels and apolipoprotein (a) (apo (a)) phenotypes in a group of urban black South African men. Design. Cross-sectional design. Setting. Lead acid battery plant, East London, Eastern Cape. Participants. Blood samples from a study on the association between lead and renal failure were kindly donated for the present study and 111 of the donors participated (K Steyn - personal communication). Outcome measures. Lp (a) levels and apo (a) phenotypes. Results. Three groups were identified: those with normal ( 700 U/l) plasma Lp (a) concentrations. Nine apo (a) phenotypes and 26 combinations thereof could be discerned. Apart from the single- and double-band phenotypes described before, triple-band phenotypes were also present. As the Lp (a) values increased, the relative frequency of the single-band phenotype decreased, whereas the relative frequency of the double-band phenotype increased. The relative frequency of the triple-band phenotype was highest in the group with high Lp (a) concentrations. No correlation was evident between the size of the apo (a) isoforms and the Lp (a) concentrations. Conclusions. Raised plasma Lp (a) levels have been associated with coronary heart disease (CHD). In addition, it has been proposed that the apo (a) gene determined plasma Lp (a) concentrations. These studies were performed using plasma from white subjects. CHD is uncommon in black South Africans. The reason may be that, given the lack of relationship between the size of the apo (a) isoforms and the Lp (a) concentrations observed in the present study, factors other than the isoform size may determine the Lp (a) levels in this particular ethnic group.Publisher’s versio

Cosmology and two-body problem of D-branes

In this paper, we investigate the dynamics and the evolution of the scale factor of a probe Dp-brane which move in the background of source Dp-branes. Action of the probe brane is described by the Born-Infeld action and the interaction with the background R-R field. When the probe brane moves away from the source branes, it expands by power law, whose index depends on the dimension of the brane. If the energy density of the gauge field on the brane is subdominant, the expansion is decelerating irrespective of the dimension of the brane. On the other hand, when the probe brane is a Nambu-Goto brane, the energy density of the gauge field can be dominant, in which case accelerating expansion occurs for $p \leq 4$. The accelerating expansion stops when the brane has expanded sufficiently so that the energy density of the gauge field become subdominant.Comment: 6 pages, 7 figures, reference added, accepted for publication in PR

LP (a) levels and apo (a) phenotypes in urban black South African men

Objective. To investigate the lipoprotein (a) (Lp (a)) levels and apolipoprotein (a) (apo (a)) phenotypes in a group of urban black South African men.Design. Cross-sectional design.Setting. Lead acid battery plant, East London, Eastern Cape.Participants. Blood samples from a study on the association between lead and renal failure were kindly donated for the present study and 111 of the donors participated (K Steyn - personal communication).Outcome measures. Lp (a) levels and apo (a) phenotypes.Results. Three groups were identified: those with normal (<300 U/I), intermediate (300 - 700 U/I) and high (> 700 U/I) plasma Lp (a) concentrations. Nine apo (a) phenotypes and 26 combinations thereof could be discerned. Apart from the single- and double-band phenotypes described before, triple-band phenotypes were also present. As the Lp (a) values increased, the relative frequency of the single-band phenotype decreased, whereas the relative frequency of the double-band phenotype increased. The relative frequency of the triple-band phenotype was highest in the group with high Lp (a) concentrations. No correlation was evident between the size of the apo (a) isoforms and the Lp (a) concentrations.Conclusions. Raised plasma Lp (a) levels have been associated with coronary heart disease (CHD). In addition, it has been proposed that the apo (a) gene determined plasma Lp (a) concentrations. These studies were performed using plasma from white subjects. CHD is uncommon in black South Africans. The reason may be that, given the lack of relationship between the size of the apo (a) isoforms and the Lp (a) concentrations observed in the present study, factors other than the isoform size may determine the Lp (a) levels in this particular ethnic group

The hierarchy problem, radion mass, localization of gravity and 4D effective Newtonian potential in string theory on S1/Z2S^{1}/Z_{2}

We present a systematical study of brane worlds in string theory on $S^{1}/Z_{2}$. Starting with the toroidal compactification of the NS/NS sector in (D+d) dimensions, we first obtain an effective $D$-dimensional action, and then compactify one of the $(D-1)$ spatial dimensions by introducing two orbifold branes as its boundaries. By combining the Gauss-Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the 4-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza-Klein (KK) modes. With a very conservative estimation, we find that the radion mass is of the order of $10^{-2} GeV$. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the 4-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss-Codacci equations and Israel's junction conditions across a (D-1)-dimensional hypersurface, which can be either spacelike or timelike.Comment: Considerably extended, Revtex4, 19 pages, 5 figures, published in IJMPA, 25, 1661-1698 (2010

Zeta Determinant for Laplace Operators on Riemann Caps

The goal of this paper is to compute the zeta function determinant for the massive Laplacian on Riemann caps (or spherical suspensions). These manifolds are defined as compact and boundaryless $D-$dimensional manifolds deformed by a singular Riemannian structure. The deformed spheres, considered previously in the literature, belong to this class. After presenting the geometry and discussing the spectrum of the Laplacian, we illustrate a method to compute its zeta regularized determinant. The special case of the deformed sphere is recovered as a limit of our general formulas.Comment: 19 pages, 1 figur