Abstract:
This thesis presents a framework for measuring the Splashback Radius (R_sp) from observational data by developing an analytical model for mean pairwise velocity and its dispersion. We perform a convolution of the real-space two-point correlation function (2PCF) into redshift space and compare it with the observed redshift-space 2PCF. This marks the first effort to measure R_sp in three dimensions, moving beyond traditional projected correlation function methods. From simulations, we report 2D splashback radius of 1.44 +- 0.05 Mpc/h and a 3D value of 1.82 +-0.04 Mpc/h in real space. Additionally, we find that R_sp increases along the line of sight in redshift space and demonstrate improved constraints when combining projected and full 2PCF data in Fisher forecast analysis. We introduce six physically motivated parameters for our mean velocity and dispersion model, with ongoing efforts to apply this model to observational data. This work enhances our ability to extract information on velocity, anisotropy, and R_sp from galaxy surveys.
