The cluster abundance in cosmic string models for structure formation

P. P. Avelino, J. H. P. Wu, E. P. S. Shellard

Abstract
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 χ² distribution and thus has a longer tail than a Gaussian distribution. We also show that σ8 normalized using cluster abundance is consistent with the COBE normalization.

Monthly Notices of the Royal Astronomical Society
Volume 318, Page 329
October 2000