Resummed Kinetic Field Theory: general formalism and linear structure growth from Newtonian particle dynamics

In earlier work, we have developed a nonequilibrium statistical field theory description of cosmic structure formation, dubbed Kinetic Field Theory (KFT), which is based on the Hamiltonian phase-space dynamics of classical particles and thus remains valid beyond shell-crossing. Here, we present an exact reformulation of the KFT framework that allows to resum an infinite subset of terms appearing in the original perturbative expansion of KFT. We develop the general formalism of this resummed KFT, including a diagrammatic language for the resummed perturbation theory, and compute the lowest-order results for the power spectra of the dark matter density contrast and momentum density. This allows us to derive analytically how the linear growth of the largest structures emerges from Newtonian particle dynamics alone, which, to our knowledge, is the first time this has been achieved.