The original seeds for the structures we see today come from density fluctuations in the early universe. Currently, these tiny initial density fluctuations result in galaxy clusters up to around 1015 h(-1) M_. Before critical cosmological implications can be deduced, both the shape and amplitude of the fluctuation spectrum must be known. The mass function of galaxy clusters is a useful tool for calculating cosmological parameters, such as the mass fluctuation on the scale of 8h(-1) Mpc (denoted by 8). Modern cosmological parameters have been determined since Hubble discovered the expansion of the Universe (1929). However, with the development of what is known as the Standard Cosmological Model in the late 1980s, their number grew. These parameters also allow us to trace the history of the Universe back to an epoch where the densities of various species exchanged, which is thought to have last occurred before Big-Bang Nucleosynthesis at neutrino decoupling. The amplitude of density variations of 152 neighbouring clusters (z0.15) is determined using a new analytical method presented in this research. Using the Press-Shechter mass function, we analyse the rms linear variation in the mass distribution on scales of 8h(-1) Mpc, i.e. 8. For masses greater than M lim=41014 h(-1) M_, the mass function is estimated. The critical density universe has an rms density fluctuation of 0.52. The findings are similar with those obtained using various high-density universe models. The findings are consistent with those of prior studies based on various models and considerations. It’s worth noting that the Planck Collaboration’s recent findings also reveal that cosmological parameters derived from cluster number counts favour lower values of the matter density parameter m and the power spectrum amplitude 8. As a result, we’ll provide a new method for estimating cosmological parameters. The modest variance in results for critical density could be related to observational uncertainty in cluster mass estimations, which are in general not substantial.
Mohammad Shafi Khan
Government Degree College Sumbal, University of Kashmir, Srinagar, J&K, India.