Anisotropic supergravity cosmologies

Anisotropic cosmologies of Bianchi types I, II, VI₀, VII₀, VIII and IX are studied in the bosonic sector of d = 11 supergravity. Exact solutions are given for all types in s = 4 dimensions coupled to the “round” (d ? s = 7) seven-sphere solutions due to Freund, Rubin, Duff and Pope, and Englert. The generalized Kasner, the Taub-NUT-de Sitter and some “mixmaster” solutions with a cosmological constant are derived. In addition, we wish to point out that the isotropic solution given recently by Myung and Kim does not exist. Another inconsistent solution was also given by Gleiser et al.