  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.
