Amplitude of Mass Fluctuations in the Universe and the Measurement of Cosmological Parameters

Abstract

Density fluctuations in the early universe provide the initial seeds for the structures we see today. These small initial density fluctuations lead to galaxy clusters up to about 1015h-1M\(\odot\) at present. Knowledge of both the shape and amplitude of the fluctuation spectrum is needed before critical cosmological implications can be derived. The mass function of galaxy clusters is a powerful tool to determine the cosmological parameters, e.g., the mass fluctuation on the scale of 8h-1Mpc (denoted by \(\sigma\)8) . The determination of modern cosmological parameters dates back to Hubble’s discovery of the expansion of the Universe (1929). But their number increased during the late 1980s with the introduction of what is often referred to as the Standard Cosmological Model. These parameters also allow us to track the history of the Universe, back to an epoch of interchanges between the densities of the different species, believed to have last happened at neutrino decoupling, before Big-Bang Nucleosynthesis. This paper presents a new analytical method to determine amplitude of density fluctuations of 152 nearby clusters (Z\(\le\)0.15). We investigate the rms linear fluctuation in the mass distribution on scales of 8h-1Mpc i.e.\(\sigma\)8 , by using Press-Shechter mass function. The mass function is estimated for masses larger than Mlim=4X1014h-1M\(\curvearrowright\) . We find rms density fluctuation equal to 0.52 for the critical density universe. The results found are consistent with those, obtained with alternative models for the high density universe. The results agree with the previous papers obtained from different models and considerations. It is interesting to note that the recent results by Planck Collaboration have also shown that the cosmological parameters derived from cluster number counts prefer lower values of the matter density parameter \(\omega\)m and power spectrum amplitude \(\sigma\)8 This takes us to introduce a new approach to estimate the cosmological parameters. For critical density, the slight variation in results may be due to the fact that there are observational uncertainties in estimates of cluster masses, which are in general not negligible.