Timelike Killing vectors are associated with conservation of energy, and space-like Killing vectors with the conservation of momentum quantities. But the energy-momentum tensor is always 'conserved' - well in GR, this goes to it's divergence being zero. And , the FRW metric does not possess a time-like Killing vector - so energy is not conserved. It possess space-like ones, and momentum is thus conserved. But, how then, is the energy-momentum tensor conserved? Depending on the geometry of the space, are there cases when momentum and energy are conserved seperately, and so energy-momentum is conserved, but also cases where the energy-momentum is only conserved as a single quantity. So a Killing vector could not suffice to give this conserved quantity. Instead would it be described by a Killing tensor? Thanks in advance.