Title: Second-order stochastic theory for self-interacting scalar fields in de Sitter spacetime

Abstract: The study of scalar field theory in de Sitter spacetime is of great importance in many facets of inflationary cosmology; however current techniques in QFT have some problems that seriously limit its computational power. Instead, we turn to effective theories. One such theory is the stochastic approach, where one utilises the inflationary expansion to write the scalar field equations in a stochastic framework. In much of the literature, the stochastic approach is applied in the “overdamped” limit, where one neglects the field momentum contribution in the equations of motion such that the stochastic equations are one-dimensional. This vastly simplifies much of the calculations but has its limits. In this talk, I will consider the full second-order stochastic equations. Focussing on the computation of the scalar correlation function, I will show that these equations have the power to give results that not only align with established results from QFT and overdamped stochastic theory but that also go beyond into hitherto unexplored regimes.