Connections on soldered principal bundles

In Kaluza-Klein theory one usually computes the scalar curvature of the principal bundle manifold using the Levi-Civita connection. Here we consider a natural family of invariant connections on a soldered principal bundle which is then parallelizable and hence spinable. This 3-parameter family includes the Levi-Civita connection and the flat connection. BY varying the connection inst-ead of merely scaling the metric on the fibers, there is greater independence among the coupling constants in the scaler curvature. In particular, a large cosmological constant can be avoided in spite of tiny fibers.