  In this paper shall we endeavour to substantiate that the evolution of the
Riemann- Christoffel tensor or curvature tensor can be expressed entirely by an
arbitrary timelike vector field and that the curvature tensor returns to its
initial value with respect to change in a particular index. This implies that
Poincare's recurrence theorem is valid in this cosmological scenario. Also, it
has been shown that geodesics can diverge just as they can converge. As is
ostensible, this result indicates the existence the of a point of exclusivity -
the opposite of a singularity.
