WHEELER-DEWITT METRIC AND THE ATTRACTIVITY OF GRAVITY

We investigate the class of ultralocal metrics on the configuration sp ace of canonical gravity. It is described by a parameter alpha, where alpha = 0.5 corresponds to general relativity. For alpha less than a c ritical value the signature is positive definite, while for all other values it is indefinite. We show that in the positive definite case gr avity becomes repulsive. From the primordial helium abundance we find that alpha must lie between 0.4 and 0.55.