Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second- and higher-order because perturbative modes are sourced by products of lower-oder modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second-order. We perform much of our analysis using an index-free `vector-calculus' approach which makes manipulating tensor equations considerably simpler.Comment: 13 pages. Final version to appear in CQ

1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations

We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett, and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS space-times, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations

Eguchi-Hanson Solitons in Odd Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS$_{d+1}/Z_p$. In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.Comment: 26 pages, Late

A gravitational wave window on extra dimensions

We report on the possibility of detecting a submillimetre-sized extra dimension by observing gravitational waves (GWs) emitted by pointlike objects orbiting a braneworld black hole. Matter in the `visible' universe can generate a discrete spectrum of high frequency GWs with amplitudes moderately weaker than the predictions of general relativity (GR), while GW signals generated by matter on a `shadow' brane hidden in the bulk are potentially strong enough to be detected using current technology. We know of no other astrophysical phenomena that produces GWs with a similar spectrum, which stresses the need to develop detectors capable of measuring this high-frequency signature of large extra dimensions.Comment: 9 pages, 5 figure

1+1+2 Electromagnetic perturbations on non-vacuum LRS class II space-times: Decoupling scalar and 2-vector harmonic amplitudes

We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and Barrett \cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on non-vacuum {\it locally rotationally symmetric} (LRS) class II space-times. Ultimately, we show how to derive six real decoupled equations governing the total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new, and result from expanding the complex EM 2-vector which we defined in \cite{Burston2007} in terms of EM 2-vector harmonic amplitudes. We are then able to show that there are four precise combinations of the amplitudes that decouple, two of these are polar perturbations whereas the remaining two are axial. The remaining two decoupled equations are the generalized Regge-Wheeler equations which were developed previously in \cite{Betschart2004}, and these govern the two EM scalar harmonic amplitudes. However, our analysis generalizes this by including a full description and classification of energy-momentum sources, such as charges and currents.Comment: 9 page

Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging

Using a recently proposed gauge invariant formulation of light-cone averaging, together with adapted "geodesic light-cone" coordinates, we show how an "induced backreaction" effect emerges, in general, from correlated fluctuations in the luminosity distance and covariant integration measure. Considering a realistic stochastic spectrum of inhomogeneities of primordial (inflationary) origin we find that both the induced backreaction on the luminosity-redshift relation and the dispersion are larger than naively expected. On the other hand the former, at least to leading order and in the linear perturbative regime, cannot account by itself for the observed effects of dark energy at large-redshifts. A full second-order calculation, or even better a reliable estimate of contributions from the non-linear regime, appears to be necessary before firm conclusions on the correct interpretation of the data can be drawn.Comment: 22 pages, 4 figures. Comments and references added, Fig. 1 modified. Version accepted for publication in JCA

Delocalization of brane gravity by a bulk black hole

We investigate the analogue of the Randall-Sundrum brane-world in the case when the bulk contains a black hole. Instead of the static vacuum Minkowski brane of the RS model, we have an Einstein static vacuum brane. We find that the presence of the bulk black hole has a dramatic effect on the gravity that is felt by brane observers. In the RS model, the 5D graviton has a stable localized zero-mode that reproduces 4D gravity on the brane at low energies. With a bulk black hole, there is no such solution -- gravity is delocalized by the 5D horizon. However, the brane does support a discrete spectrum of metastable massive bound states, or quasinormal modes, as was recently shown to be the case in the RS scenario. These states should dominate the high frequency component of the bulk gravity wave spectrum on a cosmological brane. We expect our results to generalize to any bulk spacetime containing a Killing horizon.Comment: 7 pages, 6 figure

Civitas: Toward a Secure Voting System

Civitas is the first electronic voting system that is coercion-resistant, universally and voter verifiable, and suitable for remote voting. This paper describes the design and implementation of Civitas. Assurance is established in the design through security proofs, and in the implementation through information-flow security analysis. Experimental results give a quantitative evaluation of the tradeoffs between time, cost, and security.Engineering and Applied Science

Synergistic Gravity and the Role of Resonances in GRS-Inspired Braneworlds

We consider 5D braneworld models of quasi-localized gravity in which 4D gravity is reproduced at intermediate scales while the extra dimension opens up at both the very short and the very long distances, where the geometry is flat. Our main interest is the interplay between the zero mode of these models, whenever a normalizable zero mode exists, and the effects of zero energy graviton resonant modes coming from the contributions of massive KK modes. We first consider a compactified version of the GRS model and find that quasi-localized gravity is characterized by a scale for which both the resonance and the zero mode have significant contribution to 4D gravity. Above this scale, gravity is primarily mediated by the zero mode, while the resonance gives only minor corrections. Next, we consider an asymmetric version of the standard non-compact GRS model, characterized by different cosmological constants on each AdS side. We show that a resonance is present but the asymmetry, through the form of the localizing potential, can weaken it, resulting in a shorter lifetime and, thus, in a shorter distance scale for 4D gravity. As a third model exhibiting quasi-localization, we consider a version of the GRS model in which the central positive tension brane has been replaced by a configuration of a scalar field propagating in the bulk.Comment: 18 pages, 3 figures, added 1 figure, revised version as published in Class. Quant. Gra