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

Cosmological tensor perturbations in the Randall-Sundrum model: evolution in the near-brane limit

We discuss the evolution of cosmological tensor perturbations in the RSII model. In Gaussian normal coordinates the wave equation is non-separable, so we use the near-brane limit to perform the separation and study the evolution of perturbations. Massive excitations, which may also mix, decay outside the horizon which could lead to some novel cosmological signatures.Comment: 18 pages, 1 figur

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

Simulated gravity without true gravity in asymmetric brane-world scenarios

This article investigates asymmetric brane-world scenarios in the limit when the bulk gravity is negligible. We show that, even when true self gravity is negligible, local mass concentrations will be subject to a mutual attraction force which simulates the effect of Newtonian gravity in the non-relativistic limit. Cosmological and also post-Newtonian constraints are examined

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

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

Scalar perturbations in braneworld cosmology

We study the behaviour of scalar perturbations in the radiation-dominated era of Randall-Sundrum braneworld cosmology by numerically solving the coupled bulk and brane master wave equations. We find that density perturbations with wavelengths less than a critical value (set by the bulk curvature length) are amplified during horizon re-entry. This means that the radiation era matter power spectrum will be at least an order of magnitude larger than the predictions of general relativity (GR) on small scales. Conversely, we explicitly confirm from simulations that the spectrum is identical to GR on large scales. Although this magnification is not relevant for the cosmic microwave background or measurements of large scale structure, it will have some bearing on the formation of primordial black holes in Randall-Sundrum models.Comment: 17 pages, 7 figure

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

Higher order dilaton gravity: brane equations of motion in the covariant formulation

Dilaton gravity with general brane localized interactions is investigated. Models with corrections up to arbitrary order in field derivatives are considered. Effective gravitational equations of motion at the brane are derived in the covariant approach. Dependence of such brane equations on the bulk quantities is discussed. It is shown that the number of the bulk independent brane equations of motion depends strongly on the symmetries assumed for the model and for the background. Examples with two and four derivatives of the fields are presented in more detail.Comment: 32 pages, references added, discussion extended, typos corrected, version to be publishe