Cosmological constraints on cosmic-string gravitational radiation

The primordial nucleosynthesis and pulsar timing noise constraints on cosmic-string gravitational radiation are computed. The computation consists of a numerical integration of the Friedmann-Robertson-Walker Einstein equations which describe a universe containing radiation, dust, and a "one-scale"-model cosmic-string component. The procedure takes into account the effects of the annihilations of massive particle species on the equation of state of the cosmological fluid. An expression for the power emitted per mode of oscillation by a cosmic-string loop, suggested by both analytic calculations and recent numerical simulations, is used. The results of the computation are spectra of the cosmicstring gravitational radiation at nucleosynthesis and at present. Comparison of these spectra with the observed bounds on pulsar timing noise, and the observed bound on the effective number of light neutrino species permitted by the model of nucleosynthesis, allows one to exclude a range of values of $\mu$, the cosmic-string linear mass density, for certain values of $\alpha$, the size of a newly formed loop as a fraction of the particle horizon radius. We find constraints to $\mu$ which are more restrictive than any previous limit.