The Einstein equations give the effect of gravity, including the rate of universal expansion. Also needed is the Boltzmann equation, which governs the phase space evolution of photons and neutrinos. The equations are most easily solved in k -space, because in Fourier space all the k modes in the linearized Einstein, Boltzmann, and fluid equations evolve independently. At a given time it is also necessary to integrate over the 3-momentum, q , of the massive neutrinos. We carry out a full integration down to the final time without use of any free-streaming approximation.
More detail is available on the equations used for massive neutrinos.
This requires the inclusion of up to 10,000 moments l , and the integration of up to 5000 points in k .