Stochastic gravitational wave background generated by domain wall networks

In this work we study the power spectrum of the Stochastic Gravitational Wave Background produced by standard and biased domain wall networks, using the Velocity-dependent One-Scale model to compute the cosmological evolution of their characteristic scale and root-mean-squared velocity. We consider a standard radiation + $\Lambda \rm CDM$ background and assume that a constant fraction of the energy of collapsing domain walls is emitted in the form of gravitational waves. We show that, in an expanding background, the total energy density in gravitational radiation decreases with cosmic time (after a short initial period of quick growth). We also propose a two parameter model for the scale-dependence of the frequency distribution of the gravitational waves emitted by collapsing domain walls. We determine the corresponding power spectrum of the Stochastic Gravitational Wave Background generated by domain walls, showing that it is a monotonic decreasing function of the frequency for frequencies larger than that of the peak generated by the walls that have decayed most recently. We also develop an analytical approximation to this spectrum, assuming perfect linear scaling during both the radiation and matter eras, in order to characterize the dependence of the amplitude, peak frequency and slope of the power spectrum on the model parameters.