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 accurate cosmological predictions. We explore these aspects using N-body simulations. Theoretical models of the halo mass function (HMF) can be formulated without referencing a cosmological model or input power spectrum. HMF obtained from N-body simulations show systematic deviations of 5-20\% from theoretical predictions. The physical origin of deviations may result from cosmology, the power spectrum, or both. We examine HMF deviations from universality for scale-free power spectra with an Einstein-de Sitter cosmology. We demonstrate that the mass function exhibits an explicit dependence on the slope of the input power spectrum. We find that an effective index of the $\Lambda$CDM model can correspond to the HMF from scale-free cosmologies as a first approximation. Furthermore, structure formation has led to deviations from homogeneity and isotropy on scales up to at least $100$ Mpc/h, expected to affect measurements of $H_0$. We revisit this issue of the concordance model. We find a correlation between errors in $H_0$ estimates and 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. It is essential to understand the limitations of N-body simulations to avoid misinterpreting data. We show that the missing power at small scales introduces errors in the root-mean-square fluctuations and in the simulated mass function. 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.