S-Dual Gravity in the Axial Gauge
  We investigate an action that includes simultaneously original and dual gravitational fields (in the first order formalism), where the dual fields are completely determined in terms of the original fields through axial gauge conditions and partial (non-covariant) duality constraints. We introduce two kinds of matter, one that couples to the original metric, and dual matter that couples to the dual metric. The linear response of both metrics to the corresponding stress energy tensors coincides with Einstein's equations. In the presence of nonvanishing standard and dual cosmological constants a stable solution with a time independent dual scale factor exists that could possibly solve the cosmological constant problem, provided our world is identified with the dual sector of the model. 
U. Ellwanger