MG11 
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Bifurcations of nonlinear curvature Lagrangians and dark energy

The equivalence of scalar dark matter and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This finding may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy', regarded as an effective cosmological constant. [GRG 37(2005)1427.]