Bumpy power spectra and galaxy clusters

The evolution of the abundance of galaxy clusters is not a reliable measure of fl if there are features on scales of a few Mpc in the primordial power spectrum. Conversely, if we know the cosmological model parameters from ot her measurements, the cluster abundance evolution permits us to probe featu res in the power spectrum that are in the non-linear regime at the present epoch, and hence difficult to discern directly from current epoch measureme nts. We have investigated the influence of an artificially introduced Gaussian f eature on an otherwise unperturbed SCDM power spectrum on scales correspond ing to k similar to 0.4-0.8 h Mpc(-1). Using these modified spectra as an i nput to cosmological N-body simulations, we are able to show that in terms of the cluster abundance evolution a SCDM model displays characteristics si milar to an OCDM model. However, strong modifications would also be visible at a redshift of z = 0 in the dark matter power spectrum whereas minor alt erations to the usual SCDM spectrum are washed away by non-linear evolution effects. We show that alterations to the dark matter power spectrum like t hose presented in this paper do not leave any imprint in the present densit y fluctuation spectrum and the velocity distribution of galaxy clusters; ne arly all models agree with each other and do not coincide with our fiducial OCDM model, respectively. We therefore conclude that features with charact eristics such as those discussed here might not be detectable using observa tions of the galaxy power spectrum, the local cluster abundance or the larg e-scale velocity field as measured by the velocity distribution of galaxy c lusters. The only quantity that shows a pronounced difference, at the present epoch between our models under investigation, is the halo-halo correlation functi on which appears to be strongly biased with respect to an unmodified SCDM m odel. This is due to a lack of power on certain scales which subsequently m odifies the relative amplitude of high- and low-k waves. Apart from observa tions of the evolution of cluster abundance, measurements of the Lyman a fo rest at high redshift could put constraints on possible features in the pow er spectrum, too.