Gauge theory in Riem(M)

I am writing my views on a transportation of gauge theory (a sort of generalized framework for electromagnetism and the weak and strong nuclear forces) to Riem(M), which is a space whose points are "instantaneous" configuration of the Universe (in a given time-like foliation) .
Here is the abstract:
In this paper we restrict our attention to an open subset $\mathcal{M}'$ of $\riem=\mathcal{M}$, consisting solely of metrics with no global symmetry beyond the identity. Therein we have a natural principal fiber bundle (PFB) structure $\diff\hookrightarrow \M \overset{\pi}{\ra}\M/\DD$ in which we input the connection form $\omega$ implicitly defined in \cite{Ba.1}. We work out the implications of this connection in the associated bundle with typical fiber the complex line bundle over $M$.
It is at http://arxiv.org/abs/math-ph/0702061