A Closed-Form Expression for the Gravitational Radiation Rate from Cosmic Strings

We present a new formula for the rate at which cosmic strings lose energy into gravitational radiation, valid for all piecewise-linear cosmic string loops. At any time, such a loop is composed of $N$ straight segments, each of which has constant velocity. Any cosmic string loop can be arbitrarily-well approximated by a piecewise-linear loop with $N$ sufficiently large. The formula is a sum of $O(N^4)$ polynomial and log terms, and is exact when the effects of gravitational back-reaction are neglected. For a given loop, the large number of terms makes evaluation ``by hand" impractical, but a computer or symbolic manipulator yields accurate results. The formula is more accurate and convenient than previous methods for finding the gravitational radiation rate, which require numerical evaluation of a four-dimensional integral for each term in an infinite sum. It also avoids the need to estimate the contribution from the tail of the infinite sum. The formula has been tested against all previously published radiation rates for different loop configurations. In the cases where discrepancies were found, they were due to errors in the published work. We have isolated and corrected both the analytic and numerical errors in these cases. To assist future work in this area, a small catalog of results for some simple loop shapes is provided.Comment: 29 pages TeX, 16 figures and computer C-code available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-10, (section 7 has been expanded, two figures added, and minor grammatical changes made.

Stretching Wiggly Strings

How does the amplitude of a wiggle on a string change when the string is stretched? We answer this question for both longitudinal and transverse wiggles and for arbitrary equation of state, {\it i.e.}, for arbitrary relation between the tension $\tau$ and the energy per unit length $\epsilon$ of the string. This completes our derivation of the renormalization of string parameters which results from averaging out small scale wiggles on a string. The program is presented here in its entirety.Comment: Written with ReVTeX 3.0 package. Two figures are not included. Complete paper with postscript figures can be retrieved through anonymous ftp @quark.phys.ufl.edu. Get /preprints/ifthep94_4.tar.gz, gunzip and tar it. UFIFT-HEP-94-

Cosmic String Cusps with Small-Scale Structure: Their Forms and Gravitational Waveforms

We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties of the small-scale structure. We further argue that the presence of structure at cusps under most circumstances leads to the formation of loops at the size of the smallest scales. On the other hand we show that the gravitational waveform of a cusp remains generally unchanged; the primary effect of small-scale structure is to smooth out the sharp waveform emitted in the direction of cusp motion.Comment: RevTeX, 8 pages. Replaced with version accepted for publication by PR

Wiggly Relativistic Strings

We derive the equations of motion for general strings, i.e. strings with arbitrary relation between tension $\tau$ and energy per unit length $\epsilon$. The renormalization of $\tau$ and $\epsilon$ that results from averaging out small scale wiggles on the string is obtained in the general case to lowest order in the amount of wiggliness. For Nambu-Goto strings we find deviations from the equation of state $\epsilon \tau = {\rm constant}$ in higher orders. Finally we argue that wiggliness may radically modify the gauge cosmic string scenario.Comment: 10 pages, LaTeX, UFIFT-HEP-92-1

Evolution of cosmic string configurations

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: $\xi$, related to the overall string density, $\bar\xi$, the persistence length along the string, and $\zeta$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$ initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.Comment: 61 pages, requires RevTex v3.0, SUSSEX-TH-93/3-4, IMPERIAL/TP/92-93/4

Gravitational wave bursts from cusps and kinks on cosmic strings

The strong beams of high-frequency gravitational waves (GW) emitted by cusps and kinks of cosmic strings are studied in detail. As a consequence of these beams, the stochastic ensemble of GW's generated by a cosmological network of oscillating loops is strongly non Gaussian, and includes occasional sharp bursts that stand above the ``confusion'' GW noise made of many smaller overlapping bursts. Even if only 10% of all string loops have cusps these bursts might be detectable by the planned GW detectors LIGO/VIRGO and LISA for string tensions as small as $G \mu \sim 10^{-13}$. In the implausible case where the average cusp number per loop oscillation is extremely small, the smaller bursts emitted by the ubiquitous kinks will be detectable by LISA for string tensions as small as $G \mu \sim 10^{-12}$. We show that the strongly non Gaussian nature of the stochastic GW's generated by strings modifies the usual derivation of constraints on $G \mu$ from pulsar timing experiments. In particular the usually considered ``rms GW background'' is, when G \mu \gaq 10^{-7}, an overestimate of the more relevant confusion GW noise because it includes rare, intense bursts. The consideration of the confusion GW noise suggests that a Grand Unified Theory (GUT) value $G \mu \sim 10^{-6}$ is compatible with existing pulsar data, and that a modest improvement in pulsar timing accuracy could detect the confusion noise coming from a network of cuspy string loops down to $G \mu \sim 10^{-11}$. The GW bursts discussed here might be accompanied by Gamma Ray Bursts.Comment: 24 pages, 3 figures, Revtex, submitted to Phys. Rev.

Cosmic strings, loops, and linear growth of matter perturbations

We describe the detailed study and results of high-resolution numerical simulations of string-induced structure formation in open universes and those with a non-zero cosmological constant. The effect from small loops generated from the string network has also been investigated. We provide a semi-analytical model which can reproduce these simulation results. A detailed study of cosmic string network properties regarding structure formation is also given, including the correlation time, the topological analysis of the source spectrum, the correlation between long strings and loops, and the evolution of long-string and loop energy densities. For models with $\Gamma=\Omega h=0.1--0.2 and a cold dark matter background, we show that the linear density fluctuation power spectrum induced by cosmic strings has both an amplitude at$8 h^{-1}$Mpc,$\sigma_8$, and an overall shape which are consistent within uncertainties with those currently inferred from galaxy surveys. The cosmic string scenario with hot dark matter requires a strongly scale-dependent bias in order to agree with observations.Comment: 60 pages, 24 figure

Cosmological stretching of perturbations on a cosmic string

We investigate the effects of cosmological expansion on the spectrum of small-scale structure on a cosmic string. We simulate the evolution of a string with two modes that differ in wavelength by one order of magnitude. Once the short mode is inside the horizon, we find that its physical amplitude remains unchanged, in spite of the fact that its comoving wavelength decreases as the longer mode enters the horizon. Thus the ratio of amplitude to wavelength for the short mode becomes larger than it would be in the absence of the long mode.Comment: 11 pages, 5 postscript figure

Large Angular Scale CMB Anisotropy Induced by Cosmic Strings

We simulate the anisotropy in the cosmic microwave background (CMB) induced by cosmic strings. By numerically evolving a network of cosmic strings we generate full-sky CMB temperature anisotropy maps. Based on $192$ maps, we compute the anisotropy power spectrum for multipole moments $\ell \le 20$. By comparing with the observed temperature anisotropy, we set the normalization for the cosmic string mass-per-unit-length $\mu$, obtaining $G\mu/c^2=1.05 {}^{+0.35}_{-0.20} \times10^{-6}$, which is consistent with all other observational constraints on cosmic strings. We demonstrate that the anisotropy pattern is consistent with a Gaussian random field on large angular scales.Comment: 4 pages, RevTeX, two postscript files, also available at http://www.damtp.cam.ac.uk/user/defects/ to appear in Physical Review Letters, 23 September 199