Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.Comment: 16 pages, 6 figures, Revte

The Weyl tensor two-point function in de Sitter spacetime

We present an expression for the Weyl-Weyl two-point function in de Sitter spacetime, based on a recently calculated covariant graviton two-point function with one gauge parameter. We find that the Weyl-Weyl two-point function falls off with distance like r^{-4}, where r is spacelike coordinate separation between the two points.Comment: 9 pages, no figure

Simultaneous calculation of the helical pitch and the twist elastic constant in chiral liquid crystals from intermolecular torques

We present a molecular simulation method that yields simultaneously the equilibrium pitch wave number q and the twist elastic constant K2 of a chiral nematic liquid crystal by sampling the torque density. A simulation of an untwisted system in periodic boundary conditions gives the product K2q; a further simulation with a uniform twist applied provides enough information to separately determine the two factors. We test our new method for a model potential, comparing the results with K2q from a thermodynamic integration route, and with K2 from an order fluctuation analysis. We also present a thermodynamic perturbation theory analysis valid in the limit of weak chirality

Numerical study of resistivity of model disordered three-dimensional metals

We calculate the zero-temperature resistivity of model 3-dimensional disordered metals described by tight-binding Hamiltonians. Two different mechanisms of disorder are considered: diagonal and off-diagonal. The non-equilibrium Green function formalism provides a Landauer-type formula for the conductance of arbitrary mesoscopic systems. We use this formula to calculate the resistance of finite-size disordered samples of different lengths. The resistance averaged over disorder configurations is linear in sample length and resistivity is found from the coefficient of proportionality. Two structures are considered: (1) a simple cubic lattice with one s-orbital per site, (2) a simple cubic lattice with two d-orbitals. For small values of the disorder strength, our results agree with those obtained from the Boltzmann equation. Large off-diagonal disorder causes the resistivity to saturate, whereas increasing diagonal disorder causes the resistivity to increase faster than the Boltzmann result. The crossover toward localization starts when the Boltzmann mean free path relative to the lattice constant has a value between 0.5 and 2.0 and is strongly model dependent.Comment: 4 pages, 5 figure

Spinor Parallel Propagator and Green's Function in Maximally Symmetric Spaces

We introduce the spinor parallel propagator for maximally symmetric spaces in any dimension. Then, the Dirac spinor Green's functions in the maximally symmetric spaces R^n, S^n and H^n are calculated in terms of intrinsic geometric objects. The results are covariant and coordinate-independent.Comment: 7 page

Analytic Results for the Gravitational Radiation from a Class of Cosmic String Loops

Cosmic string loops are defined by a pair of periodic functions ${\bf a}$ and ${\bf b}$, which trace out unit-length closed curves in three-dimensional space. We consider a particular class of loops, for which ${\bf a}$ lies along a line and ${\bf b}$ lies in the plane orthogonal to that line. For this class of cosmic string loops one may give a simple analytic expression for the power $\gamma$ radiated in gravitational waves. We evaluate $\gamma$ exactly in closed form for several special cases: (1) ${\bf b}$ a circle traversed $M$ times; (2) ${\bf b}$ a regular polygon with $N$ sides and interior vertex angle $\pi-2\pi M/N$; (3) ${\bf b}$ an isosceles triangle with semi-angle $\theta$. We prove that case (1) with $M=1$ is the absolute minimum of $\gamma$ within our special class of loops, and identify all the stationary points of $\gamma$ in this class.Comment: 15 pages, RevTex 3.0, 7 figures available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-1

BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)

We consider the massless scalar field on the four-dimensional sphere $S^4$. Its classical action $S={1\over 2}\int_{S^4} dV (\nabla \phi)^2$ is degenerate under the global invariance $\phi \to \phi + \hbox{constant}$. We then quantize the massless scalar field as a gauge theory by constructing a BRST-invariant quantum action. The corresponding gauge-breaking term is a non-local one of the form $S^{\rm GB}={1\over {2\alpha V}}\bigl(\int_{S^4} dV \phi \bigr)^2$ where $\alpha$ is a gauge parameter and $V$ is the volume of $S^4$. It allows us to correctly treat the zero mode problem. The quantum theory is invariant under SO(5), the symmetry group of $S^4$, and the associated two-point functions have no infrared divergence. The well-known infrared divergence which appears by taking the massless limit of the massive scalar field propagator is therefore a gauge artifact. By contrast, the massless scalar field theory on de Sitter space $dS^4$ - the lorentzian version of $S^4$ - is not invariant under the symmetry group of that spacetime SO(1,4). Here, the infrared divergence is real. Therefore, the massless scalar quantum field theories on $S^4$ and $dS^4$ cannot be linked by analytic continuation. In this case, because of zero modes, the euclidean approach to quantum field theory does not work. Similar considerations also apply to massive scalar field theories for exceptional values of the mass parameter (corresponding to the discrete series of the de Sitter group).Comment: This paper has been published under the title "Zero modes, euclideanization and quantization" [Phys. Rev. D46, 2553 (1992)

A New Waveform Consistency Test for Gravitational Wave Inspiral Searches

Searches for binary inspiral signals in data collected by interferometric gravitational wave detectors utilize matched filtering techniques. Although matched filtering is optimal in the case of stationary Gaussian noise, data from real detectors often contains "glitches" and episodes of excess noise which cause filter outputs to ring strongly. We review the standard \chi^2 statistic which is used to test whether the filter output has appropriate contributions from several different frequency bands. We then propose a new type of waveform consistency test which is based on the time history of the filter output. We apply one such test to the data from the first LIGO science run and show that it cleanly distinguishes between true inspiral waveforms and large-amplitude false signals which managed to pass the standard \chi^2 test.Comment: 10 pages, 6 figures, submitted to Classical and Quantum Gravity for the proceedings of the Eighth Gravitational Wave Data Analysis Workshop (GWDAW-8

Is the squeezing of relic gravitational waves produced by inflation detectable?

Grishchuk has shown that the stochastic background of gravitational waves produced by an inflationary phase in the early Universe has an unusual property: it is not a stationary Gaussian random process. Due to squeezing, the phases of the different waves are correlated in a deterministic way, arising from the process of parametric amplification that created them. The resulting random process is Gaussian but non-stationary. This provides a unique signature that could in principle distinguish a background created by inflation from stationary stochastic backgrounds created by other types of processes. We address the question: could this signature be observed with a gravitational wave detector? Sadly, the answer appears to be "no": an experiment which could distinguish the non-stationary behavior would have to last approximately the age of the Universe at the time of measurement. This rules out direct detection by ground and space based gravitational wave detectors, but not indirect detections via the electromagnetic Cosmic Microwave Background Radiation (CMBR).Comment: 17 pages, 4 Postscript figures, uses revtex, psfig, to be submitted to PRD, minor revisions - appendix B clarified, corrected typos, added reference

Vacuum polarization near cosmic string in RS2 brane world

Gravitational field of cosmic strings in theories with extra spatial dimensions must differ significantly from that in the Einstein's theory. This means that all gravity induced properties of cosmic strings need to be revised too. Here we consider the effect of vacuum polarization outside a straight infinitely thin cosmic string embedded in a RS2 brane world. Perturbation technique combined with the method of dimensional regularization is used to calculate ${}_{vac}^{ren}$ for a massless scalar field.Comment: 8 pages, RevTeX