Higher symmetries in a class of cosmological models (Q2640920)

The author investigates the additional symmetries of solutions of the perfect-fluid Einstein equations (with the equation of state \(p=\mu)\) admitting a two-parameter abelian isometry group with spacelike orbits and involving a single arbitrary function w(u), \(u=t-x\); he notes that the only such symmetry is the hypersurface homogeneity. In that case: 1) when \(w'=0\) the perfect-fluid solution is an orthogonal Bianchi type I, admitting a simply transitive homothety group \(H_ 4\); 2) when \(w'\neq 0\), the solution is of `tilted' Bianchi-Behr type \(VI_ h\) \((h=-4)\), and its global behaviour is discussed. The author notes also that in this class of solutions, hypersurface-homogeneity necessarily follows from fluid particles having identical thermal histories.