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Curvature Singularities from Gravitational Contraction in f(R) Gravity

The discovery of the accelerated expansion of the Universe has had a vast resonance on a number of physical disciplines. In recent years several viable modified gravity models have been proposed, which naturally lead to a late-time de Sitter stage while basically reducing to General Relativity in the early Universe. We consider a contracting cloud of pressureless dust, having arbitrary mass and initial density, and discuss some aspects of these modified gravity models. We show how the increasing energy/mass density may lead to a curvature singularity and discuss the typical timescales for its development.