The growth of linear perturbations in generic defect models for structure formation

We study the growth of linear perturbations induced by a generic causal scaling source as a function of the cosmological parameters $h$, $\Omega^m_0$ and $\Omega^\Lambda_0$. We show that for wavenumbers k \gsim 0.01 h/Mpc the spectrum of density and velocity perturbations scale in a similar way to that found in inflationary models with primordial perturbations. We show that this result is independent of the more or less incoherent nature of the source, the small scale power spectrum of the source and of deviations from scaling which naturally occur at late times if $\Omega^m_0 \neq 1$.Comment: 4 pages, 2 figure

The cluster abundance in cosmic string models for structure formation

We use the present observed number density of large X-ray clusters to constrain the amplitude of matter density perturbations induced by cosmic strings on the scale of $8 h^{-1}$Mpc ($\sigma_8$), in both open cosmologies and flat models with a non-zero cosmological constant. We find a slightly lower value of $\sigma_8$ than that obtained in the context of primordial Gaussian fluctuations generated during inflation. This lower normalization of $\sigma_8$ results from the mild non-Gaussianity on cluster scales, where the one point probability distribution function is well approximated by a $\chi^2$ distribution. We use our estimate of $\sigma_8$ to constrain the string linear energy density $\mu$ and show that it is consistent with the COBE normalization.Comment: 5 pages, 2 figure