Bumpy power spectra and galaxy clusters

Abstract

The evolution of the abundance of galaxy clusters is not a reliable measure of Ω if there are features on scales of a few Mpc in the primordial power spectrum. Conversely, if we know the cosmological model parameters from other measurements, the cluster abundance evolution permits us to probe features in the power spectrum that are in the non‐linear regime at the present epoch, and hence difficult to discern directly from current epoch measurements. We have investigated the influence of an artificially introduced Gaussian feature on an otherwise unperturbed SCDM power spectrum on scales corresponding to k∼0.4–0.8 h Mpc−1. Using these modified spectra as an input to cosmological N‐body simulations, we are able to show that in terms of the cluster abundance evolution a SCDM model displays characteristics similar 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 alterations to the usual SCDM spectrum are washed away by non‐linear evolution effects. We show that alterations to the dark matter power spectrum like those presented in this paper do not leave any imprint in the present density fluctuation spectrum and the velocity distribution of galaxy clusters; nearly all models agree with each other and do not coincide with our fiducial OCDM model, respectively. We therefore conclude that features with characteristics such as those discussed here might not be detectable using observations of the galaxy power spectrum, the local cluster abundance or the large‐scale velocity field as measured by the velocity distribution of galaxy clusters. The only quantity that shows a pronounced difference, at the present epoch between our models under investigation, is the halo–halo correlation function which appears to be strongly biased with respect to an unmodified SCDM model. This is due to a lack of power on certain scales which subsequently modifies the relative amplitude of high‐ and low‐k waves. Apart from observations of the evolution of cluster abundance, measurements of the Lyman α forest at high redshift could put constraints on possible features in the power spectrum, too.

Warm dark matter versus bumpy power spectra

“…Where WDM cuts off all power exponentially below a certain threshold, we introduce here a model that has a rather narrow dip in P ( k ) and the detailed shape for the loss of power is completely different, respectively. We have shown in an earlier paper (Knebe et al 2001b) that such localized features in the matter power spectrum can obscure the interpretation of the evolution of cluster abundance as an indicator of the cosmological density parameter. In this paper we are now going to show that a similar feature (but on smaller scales) can lead to results comparable with, for instance, a WDM model.…”

“…For the Dip model we are using the same prescription to introduce a Gaussian feature into an otherwise unperturbed CDM power spectrum as outlined in Knebe et al (2001b) and hence the modified power spectrum follows the equation: where P ( k ) is the unmodified spectrum and the parameters A , σ mod , and k 0 of the dip are given in Table 1.…”

“…One possibility to reduce this power is to introduce warm dark matter (WDM, i.e. Knebe et al 2002; Bode, Ostriker & Turok 2001; Avila‐Reese et al 2001; Colin, Avila‐Reese & Valenzuela 2000). However, another way to decrease power on a certain scale is to introduce a negative feature (‘dip’) into an otherwise unperturbed CDM power spectrum.…”

Probing the primordial power spectrum with cluster number counts

“…depends, to a good approximation, on the primordial power spectrum only through its effect on ðR; zÞ [26][27][28][29][30] …”

TOOT survey and the largest structure in the universe

“…The RS powers are close to the RLF break giving this structure optimum contrast against the rest of the 7C redshift survey. For such RS, the 7C-1,2 surveys sample ~2.5x10 6 Mpc 3 , so the probability of intersecting a SS in these combined surveys is about 2.5% in standard CDM 23,24 (which predicts a number density of 10 8 Mpc 3 or ~25 SSs out to z=0.35).…”