De Sitter Brane Research Articles

Tensor perturbations from brane-world inflation with curvature effects

The brane-world scenario provides an intriguing possibility to explore the phenomenological cosmology implied by string/M theory. In this paper, we consider a modified Randall-Sundrum single brane model with two natural generalizations: a Gauss-Bonnet term in the five-dimensional bulk action as well as an induced gravity term in the four-dimensional brane action, which are the leading-order corrections to the Randall-Sundrum model. We study the influence of these combined effects on the evolution of the primordial gravitational waves generated during an extreme slow-roll inflation on the brane. The background, for the early inflationary era, is then modeled through a de Sitter brane embedded within an anti-de Sitter bulk. In this framework, we show that both effects tend to suppress the Randall-Sundrum enhancement of the amplitude of the tensor perturbations at relatively high energies. Moreover, the Gauss-Bonnet effect, relative to standard general relativity, will abruptly enhance the tensor-to-scalar ratio and break the standard consistency relation at high energies, which cannot be evaded by invoking the induced gravity effect, even though the induced gravity strength would mildly counterbalance these significant changes at high energies. We note that the brane-world model with or without the induced gravity effect fulfills the consistency relation. Finally, we discuss some implications of the observational constraints.

Excited de Sitter brane worlds localized by a kink

We reconsider, in five-dimensional space-time, the issue of thick brane localized in the extra dimension by a kink formed by a scalar field. The localization is achieved by a sine-Gordon potential. Apart from a fundamental brane (where the scalar field is a monotonic function of the extra dimension [R. Koley and S. Kar, Classical Quantum Gravity 22, 753 (2005)]), we show that a series of new solutions exist as well, labeled by the number of zeros of the scalar field. These solutions are regular, localized on the brane, and mirror-symmetric with respect to the extra dimension. They form a tower of ``excited branes''. The study of some perturbations of the solutions reveals that the new solutions are not stable. Finally, fermions are coupled to the scalar field by means of a Yukawa potential and their localization in the background of the new solutions is examined. It turns out that the excited branes can localize left and right chiral fermions either on the brane and/or in the bulk but close to the brane.

Localization of gravity and bulk matters on a thick anti–de Sitter brane

In this paper, we investigate the localization and the mass spectra of gravity and various bulk matter fields on a thick anti--de Sitter (AdS) brane, by presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schr\"odinger equations. For gravity, the potential of the KK modes tends to infinity at the boundaries of the extra dimension, which leads to an infinite number of the bound KK modes. Although the gravity zero mode cannot be localized on the AdS brane, the massive modes are trapped on the brane. The scalar perturbations of the thick AdS brane have been analyzed, and the brane is stable under the scalar perturbations. For spin-0 scalar fields and spin-1 vector fields, the potentials of the KK modes also tend to infinity at the boundaries of the extra dimension, and the characteristic of the localization is the same as the case of gravity. For spin-1/2 fermions, by introducing the usual Yukawa coupling $\ensuremath{\eta}\overline{\ensuremath{\Psi}}\ensuremath{\phi}\ensuremath{\Psi}$ with the positive coupling constant $\ensuremath{\eta}$, the four-dimensional massless left-chiral fermion and massive Dirac fermions are obtained on the AdS thick brane.

Newtonian gravity and resonance on de Sitter branes

A de Sitter (dS) brane on the boundary between two five-dimensional spacetimes is determined. We consider asymmetric scenarios with ${\mathrm{AdS}}_{5}$ (anti-de Sitter) vacua at each side of the dS brane; and as a result, a resonant mode inside of the spectrum of the gravitational fluctuations is found. We analyze the deviations to the Newtonian potential generated by the gravitational excitations, finding that, for scenarios with large values of the cosmological constants, the contribution of the resonant mode is exponentially suppressed. However, when one of the vacua is null, the resonant mode belongs to the light states set of the gravitational fluctuations and five-dimensional gravity is recovered on the dS brane.

Extra dimensions, warped compactifications and cosmic acceleration

We report on explicit cosmological solutions within the framework of an inflating de Sitter brane embedded in five- and ten-dimensional bulk spacetimes. In the specific example we study the brane tension is induced by the curvature related to the expansion of a physical 3+1 spacetime rather than by a bulk cosmological term. In a generic situation with nonzero brane tension, the expansion of the universe accelerates eventually. We also show that inflationary cosmology is possible for a wide class of metrics without violating four- and higher-dimensional null energy condition.

Accelerating universe from warped extra dimensions

Accelerating universe or the existence of a small and positive cosmological constant is probably the most pressing obstacle as well as opportunity to significantly improving the models of four-dimensional cosmology from fundamental theories of gravity, including string theory. In seeking to resolve this problem, one naturally wonders if the real world can somehow be interpreted as an inflating de Sitter brane embedded in a higher dimensional spacetime described by warped geometry. In this scenario, the four-dimensional cosmological constant may be uniquely determined in terms of two length scales: one is a scale associated with the size of extra dimensions and the other is a scale associated with the expansion rate of our universe.

Ghosts in asymmetric brane gravity and the decoupled stealth limit

We study the spectrum of gravitational perturbations around a vacuum de Sitter brane in a 5D asymmetric braneworld model, with induced curvature on the brane. This generalises the stealth acceleration model proposed by Charmousis, Gregory and Padilla (CGP) which realises the Cardassian cosmology in which power law cosmic acceleration can be driven by ordinary matter. Whenever the bulk has infinite volume we find that there is always a perturbative ghost propagating on the de Sitter brane, in contrast to the Minkowski brane case analysed by CGP. We discuss the implication of this ghost for the stealth acceleration model, and identify a limiting case where the ghost decouples as the de Sitter curvature vanishes.

Thick de Sitter brane solutions in higher dimensions

We present thick de Sitter brane solutions which are supported by two interacting phantom scalar fields in five-, six-, and seven-dimensional spacetime. It is shown that for all cases regular solutions with anti--de Sitter asymptotic (5D problem) and a flat asymptotic far from the brane (6D and 7D cases) exist. We also discuss the stability of our solutions.

Self-properties of codimension-2 braneworlds

We consider four-dimensional de Sitter, flat and anti de Sitter branes embedded in a six-dimensional bulk spacetime whose dynamics is dictated by Lovelock theory. We find, applying a generalised version of Birkhoff's theorem, that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of Lovelock theory. These are warped solitonic spaces, where the horizons of the black hole geometries correspond to the possible positions of codimension-2 branes. The horizon temperature is related via conical singularities to the tension or vacuum energy of the branes. We classify the braneworld solutions for certain combinations of bulk parameters, according to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. The bulk Lovelock theory gives an induced gravity term on the brane, which, we argue, generates four-dimensional gravity up to some distance scale. As a result, some simple solutions, such as the Lovelock corrected Schwarzschild black hole in six dimensions, are shown to give rise to self-accelerating braneworlds. We also find that several other solutions have self-tuning properties. Finally, we present regular gravitational instantons of Lovelock gravity and comment on their significance.

Instability of brane cosmological solutions with flux compactifications

We discuss the stability of the higher-dimensional de Sitter (dS) brane solutions with two-dimensional internal space in the Einstein–Maxwell theory. We show that an instability appears in the scalar-type perturbations with respect to the dS spacetime. We derive a differential relation which has a very similar structure to the ordinary laws of thermodynamics as an extension of the work for the six-dimensional model (Kinoshita et al 2007 J. Cosmol. Astropart. Phys. JCAP05(2007)018). In this relation, the area of dS horizon (integrated over the two internal dimensions) behaves exactly as the thermodynamical entropy. The dynamically unstable solutions are in the thermodynamically unstable branch. An unstable dS compactification either evolves toward a stable configuration or a two-dimensional internal space is decompactified. These dS brane solutions are equivalent to the accelerating cosmological solutions in the six-dimensional Einstein–Maxwell–dilaton theory via dimensional reduction. Thus, if the seed higher-dimensional solution is unstable, the corresponding six-dimensional solution is also unstable. From the effective four-dimensional point of view, a cosmological evolution from an unstable cosmological solution in higher dimensions may be seen as a process of the transition from the initial cosmological inflation to the current dark-energy-dominated universe.

Instability of de Sitter brane and horizon entropy in a 6D braneworld

We investigate thermodynamic and dynamical stability of a family of six-dimensionalbraneworld solutions with de Sitter branes. First, we investigate thermodynamic stability interms of de Sitter entropy. We see that the family of solutions is divided into two distinctbranches: the high-entropy branch and the low-entropy branch. By analogy with ordinarythermodynamics, the high-entropy branch is expected to be stable and the low-entropybranch to be unstable. Next, we investigate dynamical stability by analysinglinear perturbations around the solutions. Perturbations are decomposed intoscalar, vector and tensor sectors according to the representation of the 4D de Sittersymmetry, and each sector is analysed separately. It is found that when the Hubbleexpansion rates on the branes are too large, there appears a tachyonic mode in thescalar sector and the background solution becomes dynamically unstable. We showanalytically that the onset of the thermodynamic instability and that of the dynamicalinstability exactly coincide. Therefore, the braneworld model provides a new exampleillustrating close relations between thermodynamic and dynamical instability.

Coupled bulk and brane fields about a de Sitter brane

We consider the evolution of a bulk scalar field in anti-de Sitter (AdS) spacetime linearly coupled to a scalar field on a de Sitter boundary brane. We present results of a spectral analysis of the system, and find that the model can exhibit both bound and continuum resonant modes. We find that zero, one, or two bound states may exist, depending upon the masses of the brane and bulk fields relative to the Hubble length and the AdS curvature scale and the coupling strength. In all cases, we find a critical coupling above which there exists a tachyonic bound state. We show how the 5-dimensional spectral results can be interpreted in terms of a 4-dimensional effective theory for the bound states. We find excellent agreement between our analytic results and the results of a new numerical code developed to model the evolution of bulk fields coupled to degrees of freedom on a moving brane. This code can be used to model the behavior of brane-world cosmological perturbations in scenarios for which no analytic results are known.

Holographic entanglement entropy of de Sitter braneworld

We study the holographic representation of the entanglement entropy, recently proposed by Ryu and Takayanagi, in a braneworld context. The holographic entanglement entropy of a de Sitter brane embedded in an anti--de Sitter (AdS) spacetime is evaluated using geometric quantities, and it is compared with two kinds of de Sitter entropy: a quarter of the area of the cosmological horizon on the brane and entropy calculated from the Euclidean path integral. We show that the three entropies coincide with each other in a certain limit. Remarkably, the entropy obtained from the Euclidean path integral is in precise agreement with the holographic entanglement entropy in all dimensions. We also comment on the case of a five-dimensional braneworld model with the Gauss-Bonnet term in the bulk.

Inflaton perturbations in brane-world cosmology with induced gravity

We study cosmological perturbations in the brane models with an induced Einstein–Hilbertterm on a brane. We consider an inflaton confined to a de Sitter brane in a five-dimensionalMinkowski spacetime. Inflaton fluctuations excite Kaluza–Klein modes of bulk metricperturbations with mass and where is an integer. There are two branches(± branches) of solutions for the background spacetime. In the+ branch, which includes the self-accelerating universe, a resonance appears for a mode withm2 = 2H2 due to a spin-0perturbation with m2 = 2H2. The self-accelerating universe has a distinct feature becausethere is also a helicity-0 mode of spin-2 perturbations withm2 = 2H2. Inthe − branch, which can be thought as the Randall–Sundrum type brane-world withthe high energy quantum corrections, there is no resonance. At high energies,we analytically confirm that four-dimensional Einstein gravity is recovered,which is related to the disappearance of the van Dam–Veltman–Zakharovdiscontinuity in de Sitter spacetime. On sufficiently small scales, we confirm that thelinearized gravity on the brane is well described by the Brans–Dicke theory withω = 3Hrc in the− branchand ω = −3Hrc in the + branch, respectively, which confirms the existence of the ghost in the+ branch. We also study large scale perturbations. In the+ branch, the resonance induces a non-trivial anisotropic stress on the brane via theprojection of the Weyl tensor in the bulk, but no instability is shown to exist on the brane.

Tensorial perturbations in a brane with induced gravity

We calculate the amplitude of gravitational waves produced by inflation on a de Sitter brane embedded in five-dimensional anti-de Sitter bulk space-time, extending previous calculations in Randall-Sundrum type cosmology to include the effect of induced gravity corrections on the brane. These corrections arise via a term in the brane action that is proportional to the brane Ricci scalar. We find that, as in the Randall-Sundrum case, there is a mass gap between the discrete zero-mode and a continuum of massive bulk modes, which are too heavy to be excited during inflation. We give the normalisation of the zero-mode as a function of the Hubble rate on the brane and are thus able to calculate the high energy correction to the spectrum of gravitational wave (tensor) modes excited on large scales during inflation from initial vacuum fluctuations on small scales.

Quantum fluctuations on a thick de Sitter brane

We investigate quantum fluctuations on a de Sitter (dS) brane, which has its own thickness, in order to examine whether or not the finite thickness of the brane can act as a natural cut-off for the Kaluza–Klein (KK) spectrum. We calculate the amplitude of the KK modes and the bound state by using the zeta function method after a dimensional reduction. We show that the KK amplitude is finite for a given brane thickness and in the thin wall limit the standard surface divergent behavior is recovered. The strength of the divergence in the thin wall limit depends on the number of dimensions, e.g., logarithmic on a two-dimensional brane and quadratic on a four-dimensional brane. We also find that the amplitude of the bound state mode and KK modes depends on the choice of renormalization scale; and for fixed renormalization scales the bound state mode is insensitive to the brane thickness both for two- and four-dimensional dS branes.

Can thick braneworlds be self-consistent?

We discuss the backreaction of a massless, minimally coupled, quantized scalar field on a thick, two-dimensional de Sitter (dS) brane as an extension of our previous work [M. Minamitsuji, W. Naylor, M. Sasaki, hep-th/0508093]. We show that a finite brane thickness naturally regularizes the backreaction on the brane. The quantum backreaction exhibits a quadratic divergence in the thin wall limit. We also give a theoretical bound on the brane thickness, in terms of the brane self-consistency of the quantum corrected Einstein equation, namely the requirement that the size of the backreaction should be smaller than that of the background stress–energy at the center of the brane. Finally, we discuss the brane self-consistency for the case of a four-dimensional dS brane.

Ghosts in the self-accelerating brane universe

We study the spectrum of gravitational perturbations about a vacuum de Sitter brane with the induced 4D Einstein-Hilbert term, in a 5D Minkowski spacetime (DGP model). We consider solutions that include a self-accelerating universe, where the accelerating expansion of the universe is realized without introducing a cosmological constant on the brane. The mass of the discrete mode for the spin-2 graviton is calculated for various $H{r}_{c}$, where $H$ is the Hubble parameter and ${r}_{c}$ is the crossover scale determined by the ratio between the 5D Newton constant and the 4D Newton constant. We show that, if we introduce a positive cosmological constant on the brane ($H{r}_{c}>1$), the spin-2 graviton has mass in the range $0<{m}^{2}<2{H}^{2}$ and there is a normalizable brane fluctuation mode with mass ${m}^{2}=2{H}^{2}$. Although the brane fluctuation mode is healthy, the spin-2 graviton has a helicity-0 excitation that is a ghost. If we allow a negative cosmological constant on the brane, the brane fluctuation mode becomes a ghost for $1/2<H{r}_{c}<1$. This confirms the results obtained by the boundary effective action that there exists a scalar ghost mode for $H{r}_{c}>1/2$. In a self-accelerating universe $H{r}_{c}=1$, the spin-2 graviton has mass ${m}^{2}=2{H}^{2}$, which coincides with the mass of the brane fluctuation mode. Then there arises a mixing between the brane fluctuation mode and the spin-2 graviton. We argue that this mixing presumably gives a ghost in the self-accelerating universe by continuity across $H{r}_{c}=1$, although a careful calculation of the effective action is required to verify this rigorously.

Geodesic evolution and nucleation of a de Sitter brane

Within the framework of geodesic brane gravity, the deviation from general relativity is parametrized by the conserved bulk energy. The corresponding geodesic evolution/nucleation of a de Sitter brane is shown to be exclusively driven by a double-well Higgs potential, rather than by a plain cosmological constant. The (hairy) horizon serves then as the locus of unbroken ${Z}_{2}$ symmetry. The quartic structure of the scalar potential, singled out on finiteness grounds of the total (including the dark component) energy density, chooses the Hartle-Hawking no-boundary proposal.

Brane-induced gravity from asymmetric warped compactification

We show that brane-induced gravity can be realized as a low energy effective theory of brane worlds with asymmetric warped compactification. A self-accelerating universe without cosmological constant on the brane can be realized in a model where one side of the bulk has finite volume, but the other side has infinite volume. The spin-2 perturbations for brane-induced gravity and asymmetric warped compactification models have the same spectrum at low energies. For a de Sitter brane, the spin-2 graviton has mass in the range $0<{m}^{2}\ensuremath{\le}2{H}^{2}$, with ${m}^{2}=2{H}^{2}$ in the self-accelerating universe.