We consider the early time cosmology of f(R) theories in Palatini formalism
and study the conditions that guarantee the existence of homogeneous and
isotropic models that avoid the Big Bang singularity. We show that for such
models the Big Bang singularity can be replaced by a cosmic bounce without
violating any energy condition. In fact, the bounce is possible even for
pressureless dust. We give a characterization of such models and discuss their
dynamics in the region near the bounce. We also find that power-law lagrangians
with a finite number of terms may lead to non-singular universes, which
contrasts with the infinite-series Palatini f(R) lagrangian that one needs to
fully capture the effective dynamics of Loop Quantum Cosmology. We argue that
these models could also avoid the formation of singularities during stellar
gravitational collapse.Comment: 8 pages, 4 figures; added references and a short comment in sec.I