why is the redshift space correlation function smaller than the realspace correlation function at small scales and the opposite on large scales?
The realspace correlation function is a measure of the spatial distribution of galaxies in the universe, while the redshift space correlation function takes into account the observed redshift of galaxies due to the expansion of the universe. The redshift space correlation function is distorted compared to the realspace correlation function due to the effects of peculiar velocities.
The correlation function is used to study the clustering of galaxies and the distribution of matter on large scales in the universe. By measuring the clustering of galaxies at different distances from each other, scientists can infer information about the underlying cosmological model and the growth of structures in the universe.
The shape of the correlation function can reveal information about the underlying physical processes that govern the formation and evolution of galaxies and large-scale structures. For example, a steep correlation function at small scales indicates a strong clustering of galaxies, while a flat correlation function at large scales suggests a homogenous distribution of matter.
The correlation function evolves with cosmic time as the universe expands and structures grow. In the early universe, the correlation function is expected to be more uniform due to the homogenous distribution of matter, while in later times, it becomes more clustered as gravity pulls matter together to form structures.
The correlation function is typically measured by counting the number of galaxy pairs at different distances from each other and comparing it to a random distribution. This is done using large galaxy surveys such as the Sloan Digital Sky Survey or the Dark Energy Survey. The correlation function can also be obtained through theoretical models and simulations.