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We consider the Einstein-Boltzmann system for massless particles in theBianchi I space-time with scattering cross-sections in a certain range of softpotentials. We assume that the space-time has an initial conformal gaugesingularity and show that the initial value problem is well posed with datagiven at the singularity. This is understood by considering conformallyrescaled equations. The Einstein equations become a system of singular ordinarydifferential equations, for which we establish an existence theorem whichrequires several differentiability and eigenvalue conditions on the coefficientfunctions together with the Fuchsian conditions. The Boltzmann equation isregularized by a suitable choice of time coordinate, but still hassingularities in momentum variables. This is resolved by considering singularweights, and the existence is obtained by exploiting singular moment estimates.

Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity