The measurement and applications of the faint source correlation function

The galaxy two point angular correlation function has been used for decades to measure the clustering of bright galaxies, but observers had been unable to measure a significant correlation function with faint (V > 25) galaxies. These sources are so dim that both spectral and morphology measurements fail, and their identity and redshift distribution is a mystery. I used new data, simulations and statistical techniques to measure the faint source correlation function (FSCF) at subarcsecond scales in a robust manner. I showed that the FSCF is not a continuation of the correlation function of bright galaxies and is likely due to galactic physics rather than cosmic density perturbations. I showed theoretically that when gravitational lensing acts on the FSCF, it produces a redshift-dependent anisotropy which can be used to estimate the redshift distribution of the faint sources. I used simulations to show that by measuring this effect in upcoming datasets, we will be able to significantly constrain the redshift of faint sources. Finally, I used the simulation and measurement techniques I developed for measuring the FSCF to search for cosmic string lensing events and set new direct detection limits on the tension and abundance of cosmic strings which complement the indirect limits made using the Cosmic Microwave Background and pulsar timing.