Quantum Gravity as a Sum over Geometries

The theory of gravity is non-renormalizable. Thus we either have to modify the theory or to face the problem of dealing with a non-renormalizable theory if we insist that gravity should be quantized. Here we follow the latter path and define quantum gravity as a non-perturbative sum over geometries in an exceedingly simple way. The approach is background independent but neverless we "observe" in computer simulations the emergence of a four-dimensional universe which can be viewed as a classical universe with superimposed quantum fluctuations. The results might be related to the ideas of Hartle, Hawking and Vikenkin about the creation of our universe from nothing.