Probing new physics underground

Throughout the Universe we measure the gravitational effect of dark matter (DM). This DM makes up around 63% of the total matter in the Universe today and cannot be explained by the normal fundamental particles we know about already. Instead we believe there may be other particles that interact so weakly with normal matter that their effects are extremely hard to measure. Searching for DM is a difficult task requiring theoretical understanding of possible signals, unprecedented experimental sensitivity, and rigorous statistical methods to interpret the results. In this thesis we first create and test new statistical methods that are computational efficient and maintain accuracy even in the Poissonian regime. We then apply these new techniques to the direct detection (DD) of DM - the process of searching for the energy left behind on the rare occasion that DM interacts with normal matter. Unfortunately, these DD experiments are becoming increasingly expensive and complex. We therefore turned to a new DD method that, instead of looking for DM-nucleon interactions in real time, uses ancient minerals from underground to look for the cumulative effect of these interactions over time. We showed that these minerals, called paleo-detectors, could be dramatically more sensitive than current DD experiments and robust to unknown background components such as radioactivity. Finally, we turned to neutrino interactions in these minerals. In particular, we showed that paleo-detectors could potentially discover the emission of neutrinos from supernovae within our galaxy over the past one billion years.