Comment on 4D Lorentz invariance violations in the brane-world

The brane-world scenario offers the possibility for signals to travel outside our visible universe and reenter it. We find the condition for a signal emitted from the brane to return to the brane. We study the propagation of such signals and show that, as seen by a 4D observer, these signals arrive earlier than light traveling along the brane. We also study the horizon problem and find that, while the bulk signals can travel far enough to homogenize the visible universe, it is unlikely that they have a significant effect since they are redshifted in the gravitational field of the bulk black hole.Comment: 21 pages, 6 figures, REVTEX, New section adde

Brane Cosmology Solutions with Bulk Scalar Fields

Brane cosmologies with static, five-dimensional and Z_2 symmetric bulks are analysed. A general solution generating mechanism is outlined. The qualatitive cosmological behaviour of all such solutions is determined. Conditions for avoiding naked bulk singularities are also discussed. The restrictions placed on the solutions by the assumption of such a static bulk are investigated. In particular the requirement of a non-standard energy-momentum conservation law. The failure of such solutions to provide viable quintessence terms in the Friedmann equations is also discussed.Comment: 15 pages, references added, minor change

The Operator Product Expansion of the Lowest Higher Spin Current at Finite N

For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset construction. By computing the operator product expansion of this current and itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the supersymmetric WZW model. By incorporating the self-coupling constant of lowest higher spin current which is known for the general (N,k), we present the complete nonlinear operator product expansion of the lowest higher spin current with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at the quantum level. The large (N,k) 't Hooft limit and the corresponding classical nonlinear algebra are also discussed.Comment: 62 pages; the footnotes added, some redundant appendices removed, the presentations in the whole paper improved and to appear in JHE

Equivalences between spin models induced by defects

The spectrum of integrable spin chains are shown to be independent of the ordering of their spins. As an application we introduce defects (local spin inhomogeneities in homogenous chains) in two-boundary spin systems and, by changing their locations, we show the spectral equivalence of different boundary conditions. In particular we relate certain nondiagonal boundary conditions to diagonal ones.Comment: 14 pages, 16 figures, LaTeX, Extended versio

String-inspired cosmology

I discuss cosmological models either derived from, or inspired by, string theory or M-theory. In particular I discuss solutions in the low-energy effective theory and the role of the dilaton, moduli and antisymmetric form fields in the dimensionally reduced effective action. The pre big bang model is an attempt to use cosmological solutions to make observational predictions. I then discuss the effective theory of gravity found in recent brane-world models where we live on a 3-brane embedded in a five-dimensional spacetime and how the study of cosmological perturbations may enable us to test these ideas.Comment: 15 pages, 5 figures, latex with iopart, invited talk at `The Early Universe and Cosmological Observations: a Critical Review', Cape Town, July 200

No-Go Theorem for Horizon-Shielded Self-Tuning Singularities

We derive a simple no-go theorem relating to self-tuning solutions to the cosmological constant for observers on a brane, which rely on a singularity in an extra dimension. The theorem shows that it is impossible to shield the singularity from the brane by a horizon, unless the positive energy condition (rho+p >= 0) is violated in the bulk or on the brane. The result holds regardless of the kinds of fields which are introduced in the bulk or on the brane, whether Z_2 symmetry is imposed at the brane, or whether higher derivative terms of the Gauss-Bonnet form are added to the gravitational part of the action. However, the no-go theorem can be evaded if the three-brane has spatial curvature. We discuss explicit realizations of such solutions which have both self-tuning and a horizon shielding the singularity.Comment: 7 pages, 4 figures, revtex; added reference and minor correction

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

Exact Solutions in Five-Dimensional Axi-dilaton Gravity with Euler-Poincare Term

We examine the effective field equations that are obtained from the axi-dilaton gravity action with a second order Euler-Poincare term and a cosmological constant in all higher dimensions. We solve these equations for five-dimensional spacetimes possessing homogeneity and isotropy in their three-dimensional subspaces. For a number of interesting special cases we show that the solutions fall into two main classes: The first class consists of time-dependent solutions with spherical or hyperboloidal symmetry which require certain fine-tuning relations between the coupling constants of the model and the cosmological constant. Solutions in the second class are locally static and prove the validity of Birkhoff's staticity theorem in the axi-dilaton gravity. We also give a special class of static solutions, among them the well-known black hole solutions in which the usual electric charge is superseded by an axion charge.Comment: New formulas and references adde

Lorentz-violation and cosmological perturbations: a toy brane-world model

We study possible effects of Lorentz-violation on the generation of cosmological perturbations at inflation by introducing a simple inflating five-dimensional brane-world setup with violation of four-dimensional Lorentz-invariance at an energy scale $k$. We consider massless scalar field, meant to mimic perturbations of inflaton and/or gravitational field, in this background. At three-momenta below $k$, there exists a zero mode localized on the brane, whose behaviour coincides with that in four-dimensional theory. On the contrary, at three-momenta above $k$, the localized mode is absent and physics is entirely five-dimensional. As three-momenta get redshifted, more modes get localized on the brane, the phenomenon analogous to ``mode generation''. We find that for $k\gg H$, where $H$ is the inflationary Hubble scale, the spectrum of perturbations coincides with that in four-dimensional theory. For $k < H$ and time-dependent bulk parameters, the spectrum deviates, possibly strongly, from the flat spectrum even for pure de Sitter inflation.Comment: 5 figures, iopart, minor changes, appendix adde

The quantum non-linear Schrodinger model with point-like defect

We establish a family of point-like impurities which preserve the quantum integrability of the non-linear Schrodinger model in 1+1 space-time dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the space-time symmetry of the bulk scattering matrix, are also discussed.Comment: Comments on the integrability and the impurity free limit adde