Spacetime singularities in nonlocal gravity

We study at classical level two ranges of weakly nonlocal gravitational theories that are super-renormalizable or finite at quantum level. We explicitly prove that for one out of the two classes of theories all Ricci-flat spacetimes are exact vacuum solutions of the classical equations of motion (EOM). For the second class of theories the EOM are exactly solved by all these FRW spacetimes, which are sourced by a traceless energy tensor. Therefore, the Big-Bang singularity persists when the nonlocal gravity is coupled to radiation. We here prove the above statements in three simple theorems.