The greatest challenge facing theoretical physicists today is to construct a consistent and useful quantum theory of gravity. Only when such a theory is available can one begin to determine, with confidence, the nature of the cosmos in its earliest moments, when it was less than 10_43 seconds old. The reason these moments are important is that the violent fluctuations in the geometry of spacetime that were then taking place must have had a strong influence on all the other violent processes that were going on simultaneously (the Big Bang) and hence on the subsequent evolution of the Universe. Preliminary computer investigations have already been carried out on a simplified model (known as the O(1,2) sigma model) that shares some of the significant features of quantum gravity. These investigations will be completed and work will be begun on the quantized gravitational field itself.
