  We outline unimodular conformal and projective relativity (UCPR), an
extension of unimodular relativity in which the conformal and projective
structures play central roles. Under $SL(4,\mathbb{R})$ symmetry group, the
pseudo-Riemannian metric naturally decomposes into a four-volume element and a
conformal metric; and the affine connection decomposes into a one-form and a
trace-free projective connection. In UCPR, these four space-time structures are
treated as independent fields that have clear physical interpretations. A
Palatini-type variational principle for the usual general relativity Lagrangian
leads to a breakup of the Einstein field equations and the compatibility
conditions between the metric and connection. We indicate how new gravitational
theories may be generated by modifications of this Lagrangian and discuss two
such cases. Finally, we discuss possible physical consequences of our results
for quantum gravity.
