Aspects of gravitational clustering and structure formation in the Universe

Abstract

The distribution of galaxies, halo abundance, and peculiar velocities are influenced by non linear gravitational interactions, making the study of non-linear evolution crucial for accu rate cosmological predictions. Thus, it is essential to study the underlying assumptions in these processes to improve predictions like halo abundance and determination of the Hubble Lemaître constant H0. We explore these aspects using N-body simulations. The halo model can be used to make various predictions and interpretation of observations, with the halo mass function as a core ingredient. The theoretical models of mass function can be formu lated without referencing the cosmological model and input power spectrum. Mass functions obtained from N-body simulations show systematic deviations of 5-20% from theoretical pre dictions. The physical origin of deviations is complex to understand and may result from cosmology, the power spectrum, or both. To investigate the issue, we examine mass function deviations from universality for scale-free power spectra with an Einstein-de Sitter cosmol ogy. Weshowthat the mass function has explicit dependence on the slope of the input power spectrum. We extend our analysis to ΛCDM cosmologies and show that an effective index of the ΛCDM model can correspond to the mass function from scale free cosmologies as a first approximation. Our results indicate that an improved analytical theory is required to provide better fits to the mass function. Furthermore, structure formation has led to deviations from homogeneityandisotropyonscalesuptoatleast100Mpc/h,expectedtoaffectmeasurements of H0. Various efforts have been made to quantify this effect. In our second study, we revisit this issue of the concordance model. WefindacorrelationbetweenerrorsinH0 estimatesand the density around the observer. Further, our mock observations reveal that deviations of up to 5% can occur in Milky Way-sized halos. While this finding alone does not fully resolve the Hubble tension, it may account for part of it. We rely on N-body simulations for these studies. Hence, it is essential to understand their limitations to avoid misinterpreting data. We show that the missing power at small scales introduces errors in the root-mean-square fluctuations and, consequently, in the simulated mass function. These errors are expected to diminish as the scale of non-linearity increases. Our analytical calculation indicates that mode coupling between small and large scales depends on resolving collapsed halos. Therefore, accurate mode coupling estimates require sufficient halos in the simulation