The equation governing the time evolution of the number density of loops in a cosmic string network is a detailed balance determined by energy conservation. We solve this equation with the inclusion of the gravitational radiation effect, which causes the loops to shrink (and eventually decay) as time elapses. The solution approaches a scaling regime in which the total energy density in loops remains finite, converging both in the infrared and in the ultraviolet.

• Received 15 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.071601