  We consider the gravitational coupling of a scalar field, in a reformulation
of General Relativity exhibiting local GL(4) invariance at the classical level.
We compute the one-loop contribution of the scalar to the quantum effective
potential of the vierbein and find that it does not have GL(4) invariance. The
minima of the effective potential occur for a vierbein which is proportional to
the unit matrix.

High Energy Physics - Theory