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

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

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

Expert Evidence, Hearsay and Victims of Trafficking: R v Brecani 2021 EWCA Crim 731

Case commentary of the Court of Appeal ruling in R v Brecani [2021] EWCA Crim 731

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