Non-diagonal G(2) separable perfect-fluid spacetimes

We consider non-diagonal inhomogeneous cosmologies admitting an Abelian orthogonally transitive two-dimensional group of isometries under the assumption of separation of variables. We find all the sets of compatible systems of ordinary equations which give rise to reasonable solutions (satisfying energy conditions) and study them. It turns out that five of these families exist. Two of them represent stiff fluids with the density equal to the pressure. A third family satisfies an equation of state of the linear type p = gamma rho. Regarding the fourth family we can integrate the field equations so that there only remains an ordinary differential equation for an unknown to be solved. We also give some explicit particular solutions in this case, The fifth family contains an explicit singularity-free stiff fluid solution which has already been studied by Mars in 1995 and an explicit singularity-free family satisfying the dominant energy condition (but not the strong energy condition) and which is eternally expanding and contracting without passing any big bang or big crunch.