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 8h−1Mpc (σ8), in both open cosmologies and flat models with a non-zero cosmological constant. We find a slightly lower value of σ8 than that obtained in the context of primordial Gaussian fluctuations generated during inflation. This lower normalization of σ8 results from the mild non-Gaussianity on cluster scales, where the one point probability distribution function is well approximated by a χ distribution. We use our estimate of σ8 to constrain the string linear energy density μ and show that it is consistent with the COBE normalization.