We investigate the stability of general-relativistic boson stars by classifying singularities of differential mappings and compare it with the results of perturbation theory. Depending on the particle number, the star has the following regimes of beh
avior: stable, metastable, pulsation, and collapse.
A possible equivalence of scalar dark matter, the inflaton, 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 Einstein
ian spaces, distinguished only by a different effective 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 `triple unification 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, and inflation.
