Defocusing of Null Rays in Infinite Derivative Gravity
  Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any Ansatz-dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies within an infinite derivative theory of gravity, without assuming any Ansatz to solve the full equations of motion. 
Aindri\'u Conroy, Alexey S. Koshelev and Anupam Mazumdar
gr-qc hep-th