Multiple-scales analysis of cosmological perturbations in brane-worlds

We present a new approximation method for solving the equations of motion for cosmological tensor perturbations in a Randall-Sundrum brane-world model of the type with one brane in a five-dimensional anti-de Sitter spacetime. This method avoids the problem of coordinate singularities inherent in some methods. At leading order, the zero-mode solution replicates the evolution of perturbations in a four-dimensional Friedmann-Robertson-Walker universe in the absence of any tensor component to the matter perturbation on the brane. At next order, there is a mode-mixing effect, although, importantly, the zero-mode does not source any other modes.Comment: 13 pages, Revte

Coupled boundary and bulk fields in anti-de Sitter

We investigate the dynamics of a boundary field coupled to a bulk field with a linear coupling in an anti-de Sitter bulk spacetime bounded by a Minkowski (Randall-Sundrum) brane. An instability criterion for the coupled boundary and bulk system is found. There exists a tachyonic bound state when the coupling is above a critical value, determined by the masses of the brane and bulk fields and AdS curvature scale. This bound state is normalizable and localised near the brane, and leads to a tachonic instability of the system on large scales. Below the critical coupling, there is no tachyonic state and no bound state. Instead, we find quasi-normal modes which describe stable oscillations, but with a finite decay time. Only if the coupling is tuned to the critical value does there exist a massless stable bound state, as in the case of zero coupling for massless fields. We discuss the relation to gravitational perturbations in the Randall-Sundrum brane-world.Comment: 12 pages, 4 figures, revtex

Brane-world inflation: slow-roll corrections to the spectral index

We quantify the slow-roll corrections to primordial density perturbations arising from inflation driven by a four-dimensional scalar field with a monomial potential in a five-dimensional non-compact bulk spacetime. Although the difference between the classical brane-world solutions and standard four-dimensional solutions is large at early times, the change to the amplitude at late times of perturbations generated from quantum fluctuations is first-order in slow-roll parameters, leading to second-order slow-roll corrections to the spectral index. This confirms that the leading-order effects are correctly given by previous work in the literature.Comment: 6 pages, 1 figur

Linearized self-forces for branes

We compute the regularized force density and renormalized action due to fields of external origin coupled to a brane of arbitrary dimension in a spacetime of any dimension. Specifically, we consider forces generated by gravitational, dilatonic and generalized antisymmetric form-fields. The force density is regularized using a recently developed gradient operator. For the case of a Nambu--Goto brane, we show that the regularization leads to a renormalization of the tension, which is seen to be the same in both approaches. We discuss the specific couplings which lead to cancellation of the self-force in this case.Comment: 15 page

Optimization and comparison of flux-concentrating Nd-Fe-B generator considering variable power factor and wind conditions for a 6MW offshore wind turbine

A large proportion of offshore wind turbine designs are now based on directly driven permanent magnet synchronous generators using rare earth materials. During last few years, the price of Nd-Fe-B has increased and fluctuated significantly. The large price fluctuations encourage us to look at flux-concentrating Nd-Fe-B generator (where flux-concentrating characteristics helps to increase flux density in the air gap) and optimize that for offshore wind turbine generator. In this paper, a 6 MW generator using Nd-Fe-B magnet is designed analytically in MATLAB, where magnets are placed between magnetically conducting pole shoes to reinforce the air gap flux. The generator design is optimized for the best performance machine and lowest cost of energy. Further optimization is performed to compare the results with a 6 MW surface-mounted Nd-Fe-B generator. It is found that, the flux-concentrating Nd-Fe-B generator gives better cost of energy compare to surface mounted Nd-Fe-B generator. The effect of variable power factor and sensitivity to wind conditions are also estimated in this study

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 behaviour of braneworld cosmological perturbations in scenarios for which no analytic results are known.Comment: 16 pages, 10 figures; minor ammendments to the text, typos corrected including a misprint in Eq. (102), reference adde

Primordial perturbations from slow-roll inflation on a brane

In this paper we quantise scalar perturbations in a Randall-Sundrum-type model of inflation where the inflaton field is confined to a single brane embedded in five-dimensional anti-de Sitter space-time. In the high energy regime, small-scale inflaton fluctuations are strongly coupled to metric perturbations in the bulk and gravitational back-reaction has a dramatic effect on the behaviour of inflaton perturbations on sub-horizon scales. This is in contrast to the standard four-dimensional result where gravitational back-reaction can be neglected on small scales. Nevertheless, this does not give rise to significant particle production, and the correction to the power spectrum of the curvature perturbations on super-horizon scales is shown to be suppressed by a slow-roll parameter. We calculate the complete first order slow-roll corrections to the spectrum of primordial curvature perturbations.Comment: 23 pages, 10 figure

Cosmological expansion on a dilatonic brane-world

In this paper we study brane-world scenarios with a bulk scalar field, using a covariant formalism to obtain a 4D Einstein equation via projection onto the brane. We discuss, in detail, the effects of the bulk on the brane and how the scalar field contribute to the gravitational effects. We also discuss choice of conformal frame and show that the frame selected by the induced metric provides a natural choice. We demonstrate our formalism by applying it to cosmological scenarios of Randall-Sundrum and Horava-Witten type models. Finally we consider the cosmology of models where the scalar field couples non-minimally to the matter on the brane. This gives rise to a novel scenario where the universe expands from a finite scale factor with an initial period of accelerated expansion, thus avoiding the singularity and flatness problem of the standard big bang model.Comment: 20 pages - Version to appear in Classical and Quantum Gravity. New section added on conformal rescaling of the metric. Some other minor changes made and references adde

Einstein equations for an asymmetric brane-world

We consider a brane-world of co-dimension one without the reflection symmetry that is commonly imposed between the two sides of the brane. Using the coordinate-free formalism of the Gauss-Codacci equations, we derive the effective Einstein equations by relating the local curvature to the matter on the brane in the case when its bare tension is much larger than the localized matter, and hence show that Einstein gravity is a natural consequence of such models in the weak field limit. We find agreement with the recently derived cosmological case, which can be solved exactly, and point out that such models can be realized naturally in the case where there is a minimally coupled form field in the bulk.Comment: 14 pages, Revte