De Sitter Brane Research Articles

Bulk quantum effects for de Sitter branes inAdS5

We investigate some issues regarding quantum corrections for de Sitter branes in a bulk AdS(5) spacetime. The one-loop effective action for a Majorana spinor field is evaluated and compared with the scalar field result. We also evaluate the cocycle function for various boundary conditions, finding that the quantum corrections naturally induce higher order curvature terms in the original action and, in general, it is not possible to eliminate the cocycle function by renormalisation. In the one brane limit care must be taken on how one extracts physical results. The effective potential is found to be zero on the conformally related cylinder. However, using the actual metric, the contribution from the cocycle function is non-zero and must be included. Subtleties with any zero modes are also discussed.

Quantum effects in a five-dimensional brane-world:creation of de Sitter branes and particles and stabilization of the induced cosmological constant

The role of quantum effects in brane-world cosmology isinvestigated. It is shown in a time-independent formulation thatquantum creation of de Sitter branes in five-dimensional (A)dSbulk occurs also taking account of the brane quantum CFT contribution. The surface action is chosen to include thecosmological constant and a curvature term. (The time-dependentformulation of quantum-corrected brane FRW equations is shown tobe convenient for comparison with Supernovae data.) Particlecreation on the de Sitter brane is estimated and is shown to beincreased due to Kaluza–Klein modes. The de Sitter braneeffective potential due to bulk quantum matter on 5D AdS spaceis found. It may be used to obtain the observable cosmologicalconstant in the minimum of the potential (stabilization). Theappearance of the entropy bounds from the bulk field equation isalso addressed.

De Sitter brane universe induced by phantom and quantum effects

Five-dimensional braneworld cosmology with de Sitter (inflationary) brane universe induced by classical and quantum matter is discussed. It is shown that negative energy phantom field with quantum CFT supports the creation of de Sitter universe. On the same time, pure phantom or dust with quantum effects, or Chaplygin gas with quantum effects may naturally lead to the occurrence of anti-de Sitter brane universe but not de Sitter one. It is also interesting that unlike to four-dimensional gravity, for phantom with (or without) quantum contribution the standard cosmological energy conditions may be effectively satisfied.

Of bounces, branes and bounds

Some recent studies have considered a Randall-Sundrum-like brane world evolving in the background of an anti-de Sitter Reissner-Nordstrom black hole. For this scenario, it has been shown that, when the bulk charge is non-vanishing, a singularity-free ``bounce'' universe will always be obtained. However, for the physically relevant case of a de Sitter brane world, we have recently argued that, from a holographic (c-theorem) perspective, such brane worlds may not be physically viable. In the current paper, we reconsider the validity of such models by appealing to the so-called ``causal entropy bound''. In this framework, a paradoxical outcome is obtained: these brane worlds are indeed holographically viable, provided that the bulk charge is not too small. We go on to argue that this new finding is likely the more reliable one.

Casimir effect in de Sitter and anti–de Sitter braneworlds

We discuss the bulk Casimir effect (effective potential) for a conformal or massive scalar when the bulk represents five-dimensional anti\char21{}de Sitter (AdS) or de Sitter (dS) space with one or two four-dimensional dS branes, which may correspond to our Universe. Using zeta regularization, the interesting conclusion is reached that for both bulks in the one-brane limit the effective potential corresponding to the massive or to the conformal scalar is zero. The radion potential in the presence of quantum corrections is found. It is demonstrated that both the dS and the AdS braneworlds may be stabilized by using the Casimir force only. A brief study indicates that bulk quantum effects are relevant for brane cosmology, because they do deform the de Sitter brane. They may also provide a natural mechanism yielding a decrease of the four-dimensional cosmological constant on the physical brane of the two-brane configuration.

Inhomogeneous Dark Radiation Dynamics on a de Sitter Brane

Assuming spherical symmetry we analyse the dynamics of an inhomogeneous dark radiation vaccum on a Randall and Sundrum 3-braneworld. Under certain natural conditions we show that the effective Einstein equations on the brane form a closed system. On a de Sitter brane and for negative dark energy density we determine exact dynamical and inhomogeneous solutions which depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial configuration. We also identify the conditions leading to the formation of a singularity or of regular bounces inside the dark radiation vaccum.

Self-tuning and de Sitter brane intersections in 6-dimensional brane models

We study the self-tuning of general brane junctions and brane networks on the 6-dimensional space-time. For the general brane junctions, there may exist one fine-tuning among the brane tensions. For the brane networks, similar to the 5-dimensional self-tuning brane models, the brane tensions can be set arbitrarily and there exists the singularity for the metric and bulk scalar. And if we want to regularize the singularity, we will introduce the fine-tuning among the brane tensions. In addition, because the 4-dimensional cosmological constant we observe may be positive and very small, we discuss the brane network with de Sitter brane intersections by introducing a bulk scalar.

Dark radiation dynamics on the brane

We investigate the dynamics of a spherically symmetric vacuum on a Randall and Sundrum 3-brane world. Under certain natural conditions, the effective Einstein equations on the brane form a closed system for spherically symmetric dark radiation. We determine exact dynamical and inhomogeneous solutions, which are shown to depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial energy configuration. We identify the conditions defining these solutions as singular or as globally regular. Finally, we discuss the confinement of gravity to the vicinity of the brane and show that a phase transition to a regime where gravity is not bound to the brane may occur at short distances during the collapse of positive dark energy density on a realistic de Sitter brane.

Newton potential in de Sitter braneworld

Using graviton correlator on de Sitter (dS) brane in 5d AdS or dS bulk we calculate the four-dimensional Newton potential. For flat brane in AdS bulk the Randall–Sundrum result is recovered. For flat brane in dS bulk the sign of sub-leading (1/r3) term in Newton potential is negative if compare with AdS bulk. In accordance with dS/CFT correspondence this indicates that dual CFT should be non-unitary (for example, higher derivative conformal theory).

Effective action for the homogeneous radion in brane cosmology

We consider cosmological two-brane models with AdS bulk, for which the radion, i.e., the separation between the two branes, is time dependent. In the case of two de Sitter branes (including Minkowski branes as a limiting case), we compute explicitly, without any approximation, the effective four-dimensional action for the radion. With the scale factor on-shell, this provides the non-perturbative dynamics for the radion. We discuss the differences between the dynamics derived from the four-dimensional action with the scale factor off-shell and the true five-dimensional dynamics.

Casimir energy for de Sitter branes in bulk AdS 5

The vacuum energy for a massless conformally coupled scalar field in a brane world set up, corresponding to de Sitter branes in a bulk anti-de Sitter spacetime, is calculated. We use the Euclidean version of the metric which can be conformally related to a metric similar in form to the Einstein universe ( S 4× R). Employing ζ-function regularisation we evaluate the one-loop effective potential and show that the vacuum energy is zero for the one brane and non-zero for the two brane configuration. We comment on the back-reaction of this Casimir energy and on the inclusion of a mass term or non-conformal coupling.

Comments on conformal stability of brane-world models

The stability of five-dimensional (5D) brane-world models under conformal perturbations is investigated. The analysis is carried out in the general case and then it is applied to particular solutions. It is shown that models with the Poincar\'e and de Sitter branes are unstable because they have a negative mass squared of gravexcitons whereas models with the anti--de Sitter branes have a positive gravexciton mass squared and are stable. It is also shown that 4D effective cosmological and gravitational constants on branes as well as gravexciton masses undergo a hierarchy: they have different values on different branes.

Quantum Radion on de Sitter Branes

The quantum fluctuation of the relative location of two (n-1)-dimensional de Sitter branes (i.e., of n spacetime dimensions) embedded in the (n+1)-dimensional anti-de Sitter bulk, which we shall call the quantum radion, is investigated at the linear perturbation level. The quantization of the radion is done by deriving the effective action of the radion. Assuming the positive tension brane is our universe, the effect of the quantum radion is evaluated by using the effective Einstein equations on the brane in which the radion contributes to the effective energy momentum tensor at the linear order of the radion amplitude. Specifically, the rms effective energy density arising from the quantum radion is compared with the background energy density. It is found out that this ratio remains small for reasonable values of the parameters of the model even without introducing a stabilizing mechanism for radion, although the radion itself has a negative mass squared and is unstable. The reason behind this phenomenon is also discussed.

Quantum cosmology, inflationary brane-world creation and dS/CFT correspondence

The creation of 4d de Sitter (inflationary) boundary gluing two d5 de Sitter bulks on the classical as well as on quantum level (with account of brane QFT via corresponding trace anomaly induced effective action) is discussed. Quantum effects decrease the classical de Sitter brane radius or create new de Sitter brane with even smaller radius. It is important that brane CFT may be chosen to be dual to one of 5d de Sitter bulks, making the explicit relation of de Sitter brane-world with dS/CFT correspondence. In this way, the localization of gravity on the brane is shown. Moving (time-dependent) de Sitter brane in d5 SdS BH is considered. In the special coordinate system where brane equations look like quantum-corrected FRW equations the comparison with similar brane equations in SAdS BH bulk is done.

Classical and quantum quintessence cosmology

This paper implements the idea of considering the instantonic creation of brane worlds whose five-dimensional bulk contains a negative cosmological constant and a scalar quintessence field with time-dependent equation of state, restricting to the case that the quintessence field couples minimally to Hilbert–Einstein gravity. We construct an Euclidean formalism, both for the four- and five-dimensional cases, singling out a Hamiltonian constraint that depends on the parameter defining the quintessence state equation. Specializing at several particular values of that parameter, we obtain solutions to the constraint equation and analyse them both classically and quantum mechanically. It is found that these solutions can represent either asymptotically anti-de-Sitter wormholes or pure anti-de-Sitter spaces whose quantum states are obtained by means of the Wheeler de Witt equation. Starting with the different five-dimensional solutions, an instantonic procedure is applied to describe the creation of geometrically equivalent inflating de Sitter branes whose quantum states are also evaluated in some cases. We thus consider the quantum state of the universe to be contributed by all the instantonic paths that correspond to these particular brane worlds.

String versus Einstein frame in an AdS/CFT induced quantum dilatonic brane-world universe

An AdS/CFT induced quantum dilatonic brane world where the 4D boundary is flat or a de Sitter (inflationary) or anti--de Sitter brane is considered. The classical brane tension is fixed but the boundary QFT produces the effective brane tension by means of the account of corresponding conformal anomaly induced effective action. This results in inducing brane worlds in accordance with the AdS/CFT setup as warped compactification. The explicit, independent construction of quantum induced dilatonic brane worlds in two frames, the string and Einstein frames, is done. Their complete equivalency is demonstrated for all quantum cosmological brane worlds under discussion, including several examples of classical brane-world black holes. This is different from quantum corrected 4D dilatonic gravity where a de Sitter solution exists in the Einstein but not in the Jordan (string) frame. The role of quantum corrections in massive graviton perturbations around an anti--de Sitter brane is briefly discussed.

Wave function of the radion in the dS and AdS brane worlds

We study the linearized metric perturbation corresponding to the radion for the generalization of the five dimensional two brane setup of Randall and Sundrum to the case when the curvature of each brane is locally constant but non-zero. We find the wave fuction of the radion in a coordinate system where each brane is sitting at a fixed value of the extra coordinate. We find that the radion now has a mass$^2$, which is negative for the case of de Sitter branes but positive for anti de Sitter branes. We also determine the couplings of the radion to matter on the branes, and construct the four dimensional effective theory for the radion valid at low energies. In particular we find that in AdS space the wave function of the radion is always normalizable and hence its effects, though small, remain finite at arbitrarily large brane separations.

De Sitter brane gravity: from close-up to panorama

We find explicitly the induced graviton propagator on de Sitter branes embedded in various five-dimensional spacetimes; de Sitter branes in AdS and Minkowski space are particular cases. By studying the structure of the momentum-space propagator, we are able to extract interesting physics, much of which is qualitatively different from that of flat branes. We find that (1) there can be a set of graviton-like particles which mediate brane gravity at different scales; (2) localized gravity can exist even on de Sitter branes in Minkowski space; (3) Kaluza–Klein modes also contribute to conventional 4D gravity for de Sitter branes in AdS; and (4) Newton's constant can vary considerably with scale. We comment on the implications for the effective cosmological constant.

Anti-de-Sitter D-branes

We study D-branes of the ${SL(2,\bR)}$ WZW model, and of its discrete orbifolds. Gluing the currents by group automorphisms leads to three types of D-branes: two-dimensional hyperbolic planes ($H_2$), de Sitter branes (dS$_2$), or anti-de-Sitter branes (AdS$_2$). We explain that the dS$_2$ branes are unphysical, because the electric field on their worldvolume is supercritical. By combining ${SL(2,\bR)}$ and SU(2), we exhibit a class of supersymmetric AdS$_2\times S^2$ three-brane worldvolumes, and consider their possible embeddings in the near-horizon region of stringy black holes. We point out the intriguing difference between the induced and the effective geometries of these D-branes, and speculate on its possible significance.

Radion on the de Sitter Brane

The radion on the de Sitter brane is investigated at the linear perturbation level, using the covariant curvature tensor formalism developed by Shiromizu, Maeda and Sasaki. It is found that if there is only one de Sitter brane with positive tension, there is no radion and thus the ordinary Einstein gravity is recoverd on the brane other than corrections due to the massive Kaluza-Klein modes. As a by-product of using the covariant curvature tensor formalism, it is immediately seen that the cosmological scalar, vector and tensor type perturbations all have the same Kaluza-Klein spectrum. On the other hand, if there are two branes with positive and negative tensions, the gravity on each brane takes corrections from the radion mode in addition to the Kaluza-Klein modes and the radion is found to have a negative mass-squared proportional to the curvature of the de Sitter brane, in contrast to the flat brane case in which the radion mass vanishes and degenerates with the 4-dimensional graviton modes. To relate our result with the metric perturbation approach, we derive the second order action for the brane displacement. We find that the radion identified in our approach indeed corresponds to the relative displacement of the branes in the Randall-Sundrum gauge and describes the scalar curvature perturbations of the branes in the gaussian normal coordinates around the branes. Implications to the inflationary brane universe are briefly discussed.