Analytic solutions for the Bianchi I universe coupled to several barotropic perfect fluids

We consider the Bianchi I geometry coupled to several species of comoving barotropic perfect fluids with a linear equation of state in the context of general relativity. The solution of the dynamics can be reduced to a quadrature, which can be explicitly performed in certain cases. In particular, we obtain the explicit solution for one species, as well as for two species, given their barotropic indices obey a certain relation. These solutions include and generalize different models studied in the literature. For completeness, we analyze all the different possible signs of the matter energy densities, and we obtain a particularly interesting model in which an exotic species produces a bounce of the scale factor, providing a singularity-free cosmology, and then decays to leave a nonexotic component as the dominant fluid for large volumes.