Characterisation of orthogonal perfect fluid cosmological spacetimes

We consider the general orthogonal metric separable in space and time variables in comoving coordinates. We then characterise perfect fluid models admitted by such a metric. It turns out that the homogeneous models can only be either FLRW or Bianchi I while the inhomogeneous ones can only admit $G_2$ (two mutually as well as hypersurface orthogonal spacelike Killing vectors) isometry. The latter can possess singularities of various kinds or none. The non-singular family is however unique and cylindrically symmetric.