The cosmological constant filter without big bang singularity

In the recently proposed cosmological constant (CC) filter mechanism based on modified gravity in the Palatini formalism, gravity in the radiation, matter and late-time de Sitter eras is insensitive to energy sources with the equation of state -1. This implies that finite vacuum energy shifts from phase transitions are filtered out too. In this work, we investigate the CC filter model at very early times. We find that the initial big bang singularity is replaced by a cosmic bounce, where the matter energy density and the curvature are finite. In a certain case, this finiteness can be already observed on the algebraic level. (paper)