The 2-point correlation function in alternative dark matter model

This thesis investigates cosmic structure formation through statistical analysis of dark matter halo clustering in high-resolution cosmological simulations. Using two-point correlation function (2PCF) measurements from IllustrisTNG (TNG100-1, TNG300-1, and their dark-matter-only counterparts) and dedicated warm dark matter (WDM) simulations, we quantify how baryonic physics and dark matter properties shape large-scale structure. The CosmoBolognaLib C++ library enables efficient 2PCF computation in real/redshift space, incorporating integral constraint corrections for finite-volume effects. Key findings reveal: mass-dependent clustering: massive halos show stronger clustering in dense cosmic web environments compared to uniformly distributed low-mass halos; baryonic impact: hydrodynamical runs exhibit enhanced clustering in filaments/knots versus dark-matter-only simulations; WDM signatures: free-streaming effects suppress low-mass subhalos while increasing small-scale clustering of surviving halos, with 2PCF profiles showing: reduced amplitude at <1 Mpc/h, stronger residuals from linear bias models; scale-dependent structure suppression. Discrepancies between simulations and theory emerge at both small (<1 Mpc/h, from unmodeled baryonic processes) and large scales (>30 Mpc/h, due to box-size limitations). These results emphasize the need for improved nonlinear regime models incorporating baryonic feedback and hydrodynamical effects. Our work provides critical insights for interpreting upcoming Euclid and DESI survey data. Future directions include machine learning-enhanced bias modeling, larger simulation volumes, and higher-order statistics (e.g., 3-point correlations) to capture cosmic web non-Gaussianity.