Kinetic Field Theory: Perturbation theory beyond first order

We present recent improvements in the perturbative treatment of particle interactions in Kinetic Field Theory (KFT) for inertial Zel'dovich trajectories. KFT has been developed for the systematic analytical calculation of non-linear cosmic structure formation on the basis of microscopic phase-space dynamics. We improve upon the existing treatment of the interaction operator by deriving a more rigorous treatment of phase-space trajectories of particles in an expanding universe. We then show how these results can be applied to KFT perturbation theory by calculating corrections to the late-time dark matter power spectrum at second order in the interaction operator. We find that the modified treatment of interactions w.r.t. inertial Zel'dovich trajectories improves the agreement of KFT with simulation results on intermediate scales compared to earlier results. Additionally, we illustrate that including particle interactions up to second order leads to a systematic improvement of the non-linear power spectrum compared to the first-order result.