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Recently,1-3 it is shown that, the quantum effects of matter are well described by the conformal degree of freedom of the space-time metric. On the other hand, it is a well-known fact that according to Einstein's gravity theory, gravity and geometry are interconnected. In the new quantum gravity theory,1-3 matter quantum effects completely determine the conformal degree of freedom of the space-time metric, while the causal structure of the space-time is determined by the gravitational effects of the matter, as well as the quantum effects through back reaction effects. This idea, previously, is realized in the framework of scalar-tensor theories. In this work, it is shown that quantum gravity theory can also be realized as a purely metric theory. Such a theory is developed, its consequences and its properties are investigated. The theory is applied, then, to black holes and the radiation-dominated universe. It is shown that the initial singularity can be avoided.
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