  The theory of Ratio Gravity (RG) proposes that the curvature of 3+1 spacetime
originates from a deformation of a Cross Ratio, where similar mathematical
structure to general relativity emerges. This paper studies RG using the
framework of the Newman-Penrose spin formalism. After proposing the general
formalism, we move on to study a homogeneous and isotropic universe with RG. It
is noted that the theory contains a component of dynamical dark energy with
novel equation of state.
