Compact stars in Eddington inspired gravity

A new, Eddington inspired theory of gravity was recently proposed by Ba?ados and Ferreira. It is equivalent to general relativity in vacuum, but differs from it inside matter. This viable, one-parameter theory was shown to avoid cosmological singularities and turns out to lead to many other exciting new features that we report here. First, for a positive coupling parameter, the field equations have a dramatic impact on the collapse of dust, and do not lead to singularities. We further find that the theory supports stable, compact pressureless stars made of perfect fluid, which provide interesting models of self-gravitating dark matter. Finally, we show that the mere existence of relativistic stars imposes a strong, near optimal constraint on the coupling parameter, which can even be improved by observations of the moment of inertia of the double pulsar.