Cosmic Strings - Dead Again?

I report on recent numerical simulations of the simplest field theory with cosmic string solutions, the Abelian Higgs model. We find that random networks of string quickly converge to a scaling solution in which the network scale length $\xi$ increases linearly with time. There are very few loops with sizes less than $\xi$, and the strings are smooth, showing no signs of ``small scale structure''. We claim that particle production is the dominant energy-loss mechanism, not gravitational radiation as previously thought. For strings in Grand Unified Models, stringent constraints can be placed from cosmic ray observations on the string tension $\mu$: we estimate $G\mu < 10^{-9}$, three orders of magnitude lower than the constraint from Cosmic Microwave Background fluctuations.Comment: Late appearance of talk given at Cosmo 97, Ambleside, England, Sept 97, based on hep-ph/9708427 (error concerning UHE cosmic ray bounds addressed). 4pp, 1eps fig, LaTeX2

The Origin of the Sphaleron Dipole Moment

By providing a suitable definition of the electromagnetic field off the Higgs vacuum, we show that within the sphaleron there is a monopole-antimonopole pair with quantized charges, and a loop of electromagnetic current. On integration of the relevant charges and currents over the interior in the limit of small $\Theta_W$, we recover the standard formula for the sphaleron dipole moment.Comment: 13pp Plain TeX, 2 ps figures in 2 files, self-unpacking uuencoded. (Tidied up, discussion of 't Hooft definition of electromagnetic charge, and 2 nice new figures showing charge and current distributions inside the sphaleron.

Asymptotically Safe Cosmology

We study quantum modifications to cosmology in a Friedmann-Robertson-Walker universe with and without scalar fields by taking the renormalisation group running of gravitational and matter couplings into account. We exploit the Bianchi identity to relate the renormalisation group scale with scale factor and derive the improved cosmological evolution equations. We find two types of cosmological fixed points where the renormalisation group scale either freezes in, or continues to evolve with scale factor. We discuss the implications of each of these, and classify the different cosmological fixed points with and without gravity displaying an asymptotically safe renormalisation group fixed point. We state conditions of existence for an inflating ultraviolet cosmological fixed point for Einstein gravity coupled to a scalar field. We also discuss other fixed point solutions such as "scaling" solutions, or fixed points with equipartition between kinetic and potential energies.Comment: 8 pages; v2: explanations and references added, accepted for publication in JCA

CMB temperature trispectrum of cosmic strings

We provide an analytical expression for the trispectrum of the cosmic microwave background (CMB) temperature anisotropies induced by cosmic strings. Our result is derived for the small angular scales under the assumption that the temperature anisotropy is induced by the Gott-Kaiser-Stebbins effect. The trispectrum is predicted to decay with a noninteger power-law exponent l(-rho) with 6 &lt; rho &lt; 7, depending on the string microstructure, and thus on the string model. For Nambu-Goto strings, this exponent is related to the string mean square velocity and the loop distribution function. We then explore two classes of wave number configuration in Fourier space, the kite and trapezium quadrilaterals. The trispectrum can be of any sign and appears to be strongly enhanced for all squeezed quadrilaterals

A possible origin of superconducting currents in cosmic strings

The scattering and capture of right-handed neutrinos by an Abelian cosmic string in the SO(10) grand unification model are considered. The scattering cross-section of neutrinos per unit length due to the interaction with the gauge and Higgs fields of the string is much larger in its scaling regime than in the friction one because of the larger infrared cutoff of the former.The probability of capture in a zero mode of the string accompanied by the emission of a gauge or Higgs boson shows a resonant peak for neutrino momentum of the order of its mass. Considering the decrease of number of strings per unit comoving volume in the scaling epoch the cosmological consequences of the superconducting strings formed in this regime will be much smaller than those which could be produced already in the friction one.Comment: 14 pages Latex, 4 figues/ep

Cosmological Perturbations from Cosmic Strings

Some aspects of the theory of cosmological perturbations from cosmic strings and other topological defects are outlined, with particular reference to a simple example: a spatially flat CDM-dominated universe. The conserved energy-momentum pseudo-tensor is introduced, and the equation for the density perturbation derived from it. It is shown how the scaling hypothesis for defect evolution results in a Harrison-Zel'dovich spectrum for wavelengths well inside the horizon.Comment: LaTeX, 6pp. From Proceedings of `Trends in Astroparticle Physics', Stockholm, Sweden 22-25 September 1994, edited by L. Bergstr\"om, P. Carlson, P.O. Hulth and H. Snellman (to be published in Nucl.~Phys~B, Proceedings Supplements Section