THE SOLUTIONS OF THE COSMIC-STRING LOOP EQUATION IN AN EXPANDING UNIVERSE

The cosmic string loop equation is studied analytically during the radiation-dominated era in the Robertson-Walker universe. If the loops expand with the Hubble flow at the time of formation of the loops, the cosmic string loops occur always collapsing. We also discuss the initial radii R(s)(t*) dependence of the lifetime tau(s) without considering oscillations, as a first approximation, where t* denotes the time of the formation of the loops. We find that the lifetime factor gamma=ctau(s)/R(s)(t*) is tau/2 in the limit of small initial radius.