Properties of codimension-2 braneworlds in six-dimensional Lovelock theory

We consider maximally symmetric 3-branes embedded in a six-dimensional bulk spacetime with Lovelock dynamics. We study the properties of the solutions with respect to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. Some simple solutions are shown to give rise to self-accelerating braneworlds, whereas several others solutions have self-tuning properties. For the case of geometric self-acceleration we argue that the cross-over scale in between four-dimensional and higher-dimensional gravity and the scale of late-time geometric acceleration, fixed by the present horizon size, are related via the conical deficit angle of the six-dimensional bulk solution, which is a free parameter.Comment: 6 pages, prepared for the 13th Conference on Recent Developments in Gravity (NEB XIII), Thessaloniki, Greece, 4 - 6 Jun 2008; v2: reference adde

Properties of codimension-2 braneworlds in six-dimensional Lovelock theory

We consider maximally symmetric 3-branes embedded in a six-dimensional bulk spacetime with Lovelock dynamics. We study the properties of the solutions with respect to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. Some simple solutions are shown to give rise to self-accelerating braneworlds, whereas several others solutions have self-tuning properties. For the case of geometric self-acceleration we argue that the cross-over scale in between four-dimensional and higher-dimensional gravity and the scale of late-time geometric acceleration, fixed by the present horizon size, are related via the conical deficit angle of the six-dimensional bulk solution, which is a free parameter.Comment: 6 pages, prepared for the 13th Conference on Recent Developments in Gravity (NEB XIII), Thessaloniki, Greece, 4 - 6 Jun 2008; v2: reference adde

Properties of codimension-2 braneworlds in six-dimensional Lovelock theory

We consider maximally symmetric 3-branes embedded in a six-dimensional bulk spacetime with Lovelock dynamics. We study the properties of the solutions with respect to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. Some simple solutions are shown to give rise to self-accelerating braneworlds, whereas several others solutions have self-tuning properties. For the case of geometric self-acceleration we argue that the cross-over scale in between four-dimensional and higher-dimensional gravity and the scale of late-time geometric acceleration, fixed by the present horizon size, are related via the conical deficit angle of the six-dimensional bulk solution, which is a free parameter.Comment: 6 pages, prepared for the 13th Conference on Recent Developments in Gravity (NEB XIII), Thessaloniki, Greece, 4 - 6 Jun 2008; v2: reference adde

Black holes and stars in Horava-Lifshitz theory with projectability condition

We systematically study spherically symmetric static spacetimes filled with a fluid in the Horava-Lifshitz theory of gravity with the projectability condition, but without the detailed balance. We establish that when the spacetime is spatially Ricci flat the unique vacuum solution is the de Sitter Schwarzshcild solution, while when the spacetime has a nonzero constant curvature, there exist two different vacuum solutions; one is an (Einstein) static universe, and the other is a new spacetime. This latter spacetime is maximally symmetric and not flat. We find all the perfect fluid solutions for such spacetimes, in addition to a class of anisotropic fluid solutions of the spatially Ricci flat spacetimes. To construct spacetimes that represent stars, we investigate junction conditions across the surfaces of stars and obtain the general matching conditions with or without the presence of infinitely thin shells. It is remarkable that, in contrast to general relativity, the radial pressure of a star does not necessarily vanish on its surface even without the presence of a thin shell, due to the presence of high order derivative terms. Applying the junction conditions to our explicit solutions, we show that it is possible to match smoothly these solutions (all with nonzero radial pressures) to vacuum spacetimes without the presence of thin matter shells on the surfaces of stars.Comment: The relations between energy-momentum tensors used in HL theory and GR are considered, and the singular behavior of the trace of extrinsic curvature is presented. References are updated. Version to appear in Physical Reviews D

The consistency of codimension-2 braneworlds and their cosmology

We study axially symmetric codimension-2 cosmology for a distributional braneworld fueled by a localised 4D perfect fluid, in a 6D Lovelock theory. We argue that only the matching conditions (dubbed topological) where the extrinsic curvature on the brane has no jump describe a pure codimension-2 brane. If there is discontinuity in the extrinsic curvature on the brane, this induces inevitably codimension-1 distributional terms. We study these topological matching conditions, together with constraints from the bulk equations evaluated at the brane position, for two cases of regularisation of the codimension-2 defect. First, for an arbitrary smooth regularisation of the defect and second for a ring regularisation which has a cusp in the angular part of the metric. For a cosmological ansatz, we see that in the first case the coupled system is not closed and requires input from the bulk equations away from the brane. The relevant bulk function, which is a time-dependent angular deficit, describes the energy exchange between the brane and the 6D bulk. On the other hand, for the ring regularisation case, the system is closed and there is no leakage of energy in the bulk. We demonstrate that the full set of matching conditions and field equations evaluated at the brane position are consistent, correcting some previous claim in the literature which used rather restrictive assumptions for the form of geometrical quantities close to the codimension-2 brane. We analyse the modified Friedmann equation and we see that there are certain corrections coming from the non-zero extrinsic curvature on the brane. We establish the presence of geometric self-acceleration and a possible curvature domination wedged in between the period of matter and self-acceleration eras as signatures of codimension-2 cosmology.Comment: 21 pages, 5 figures, journal versio

Multi-Brane Worlds and modification of gravity at large scales

We discuss the implications of multi-brane constructions involving combinations of positive and negative tension brane and show how anomalously light KK states emerge when negative tension ''-'' branes are sandwiched between ''+'' branes. We present a detailed study of a ''+--+'' brane assignment which interpolates between two models that have been previously proposed in which gravity is modified at large scales due to the anomalously light states. We show that it has the peculiar characteristic that gravity changes from four dimensional (4D) to 5D at large distances and returns to 4D at even larger scales. We also consider a crystalline universe which leads to a similar structure for gravity. The problems associated with intermediate negative tension branes are discussed and a possible resolution suggested.Comment: 28 pages, 6 figures,references adde

Anisotropic Extra Dimensions

We consider the scenario where in a five-dimensional theory, the extra spatial dimension has different scaling than the other four dimensions. We find background maximally symmetric solutions, when the bulk is filled with a cosmological constant and at the same time it has a three-brane embedded in it. These background solutions are reminiscent of Randall-Sundrum warped metrics, with bulk curvature depending on the parameters of the breaking of diffeomorphism invariance. Subsequently, we consider the scalar perturbation sector of the theory and show that it has certain pathologies and the striking feature that in the limit where the diffeomorphism invariance is restored, there remain ghost scalar mode(s) in the spectrum.Comment: 12 pages, no figures, comments and references added, published versio

Codimension-2 brane inflation

We consider a probe codimension-2 brane inflation scenario in a warped six-dimensional flux compactification. Our background model is Salam-Sezgin gauged supergravity with codimension-2 brane sources, which preserve N=1 supersymmetry. The model has a modulus, which is stabilised by means of a cap regularisation of the codimension-2 singularities, with appropriate dilaton potentials on the ring interface of the caps with the bulk. We discuss the cosmological evolution of the world-volume of a probe codimension-2 brane when it moves along the radial direction of the internal space. In order to have slow-roll inflation, one needs the warping of the internal space to be weak, in contrast to the recent string inflation constructions with strong warping. We discuss the parameter range that the inflation is in agreement with the observationally inferred parameters and which furthermore is consistent with the probe brane approximation. We provide arguments pointing that the probe brane approximation is a good assumption if the probe brane is not exactly conical and show with a multibrane solution that the mild warping needed for a slow-roll inflation is not spoiled by the probe brane.Comment: 38 pages, 1 figure, Journal version in Phys. Rev.

The m->0 limit for massive graviton in dS_4 and AdS_4. How to circumvent the van Dam-Veltman-Zakharov discontinuity

We show that, by considering physics in dS_4 or AdS_4 spacetime, one can circumvent the van Dam - Veltman - Zakharov theorem which requires that the extra polarization states of a massive graviton do not decouple in the massless limit. It is shown that the smoothness of the m->0 limit is ensured if the H (``Hubble'') parameter, associated with the horizon of the dS_4 or AdS_4 space, tends to zero slower than the mass of the graviton m.Comment: 11 pages, references added, minor typos correcte