  We investigate the one-loop infrared behaviour of the effective potential in
minimally coupled graviton Higgs theory in Minkowski background. The
gravitational analogue of one loop Coleman Weinberg effective potential turns
out to be complex, the imaginary part indicating an infrared instability. This
instability is traced to a tachyonic pole in the graviton propagator for
constant Higgs fields. Physical implications of this behaviour are studied. We
also discuss physical differences between gauge theories coupled to Higgs
fields and graviton Higgs theory.
