(ed.). Gravitational waves (IOP, 2001)(422s).

218 Sources of SGWB-5-6-7-8-9-10 0 10Figure 13.2. The spectrum of gravitational radiation produced by a string network for agiven set of dimensionless parameters.We are now in a position to construct the differential equation describingthe rate of change of the energy in loops present in a volume V (t) at time t.The numerical integration of this equation and the method applied to calculatethe power spectrum of gravitational radiation are discussed in detail in [34].The results of this calculation are shown in figure 13.2. In this paper analyticexpressions for the latter have also been derived. Even though simplified forconvenience, these analytic expressions offer the opportunity to examine thevarious dependences of the spectrum on string and cosmological parameters.The spectrum of gravitational radiation produced by a network of strings hastwo main features:• A nearly equal gravitational radiation energy density per logarithmicfrequency interval in the range (10 −8 , 10 10 ) Hz. This portion (‘red noise’)of the spectrum corresponds to GWs emitted during the radiation-dominatedera and does not show a significant dependence by the spectral index q andthe cut-off n ∗ [35].