  We study S-duality transformations that mix the Riemann tensor with the field
strength of a 3-form field. The dual of an (A)dS space time - with arbitrary
curvature - is seen to be flat Minkowski space time, if the 3-form field has
vanishing field strength before the duality transformation. It is discussed
whether matter could couple to the dual metric, related to the Riemann tensor
after a duality transformation. This possibility is supported by the facts that
the Schwarzschild metric can be obtained as a suitable contraction of the dual
of a Taub-NUT-AdS metric, and that metrics describing FRW cosmologies can be
obtained as duals of theories with matter in the form of torsion.
