According to the standard paradigm, inflation seeded the primordial Universe with density perturbations that are adiabatic and Gaussian distributed. In this limit, all the information is contained within the two-point correlation function, or equivalently, the power spectrum. Today, the distribution of matter is far from Gaussian, with structures forming across a vast range of scales. Despite this, almost all analyses of observational data are performed using two-point functions. This begs the question: what information lies in higher-point statistics?
In this seminar, I will present a pedagogical overview of the non-Gaussian correlation functions, and demonstrate how they can be used both to sharpen constraints on known physical parameters, and to provide stringent tests of new physics occurring in the early Universe. One of the major barriers to constraining cosmology from the higher-point functions is computational: measuring the statistics with conventional techniques is infeasible for current and future datasets. I will discuss new methods capable of reducing the computational cost by orders of magnitude, and show how this facilitates a number of exciting new tests of the cosmological model.