Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories

We present cosmological perturbations of kinetic components based on relativistic Boltzmann equations in the context of generalized gravity theories. Our general theory considers an arbitrary number of scalar fields generally coupled with gravity, an arbitrary number of mutually interacting hydrodynamic fluids, and components described by the relativistic Boltzmann equations such as massive or massless collisionless particles and the photon with the accompanying polarizations. We also include direct interactions among fluids and fields. The background Friedmann-Lemaître-Robertson-Walker model includes the general spatial curvature and the cosmological constant. We consider three different types of perturbation, and all the scalar-type perturbation equations are arranged in a gauge-ready form so that one can easily implement convenient gauge conditions depending on the situation. In the numerical calculation of the Boltzmann equations we have implemented four different gauge conditions in a gauge-ready manner where two of them are new. By comparing solutions obtained separately in different gauge conditions we can naturally check the numerical accuracy.