Kinetic Field Theory. Momentum-density correlations and fuzzy dark matter

Building upon the recent developments of Kinetic Field Theory (KFT) for cosmic structure formation we develop a systematic way to calculate correlation functions of the momentum-density field. We show that these correlators can be calculated from the factorised generating functional after application of partial derivatives with respect to the momentum shift. For visual aid and in order to facilitate an automatic evaluation of corrections by particle interactions we introduce a diagrammatic representation of terms. We employ this formalism to calculate the 2-point momentum-density correlation tensor including initial correlations to quadratic order and completely. A comparison of the results shows that the initial correlations are responsible for the deformation of the power-spectrum on small scales rather than the particle interactions. In the spirit of the Born approximation we use an effective force term to calculate the corrections due to gravity. Our results are in good agreement with previous analytic and simulation results. Recently, Fuzzy Dark Matter models such as Ultra-Light Axions have caught a lot of interest. Their dynamics is described by the classical equations of a condensate. This introduces a quantum potential in the Euler equation and is generally repulsive. We have developed an extension to KFT treating the effects of the quantum potential on the dynamics and on the initial density fluctuation power-spectrum. We find the effects to be largest on scales in the range of 3h/M>or similar k>or similar 0.3h/Mpc, close to the onset of non-linear structures.