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The question: ,,what is the structure of the universe at the Planck scale (lO^-35 m)" is a long-standing problem of theoretical physics. We can expect that at this scale the spacetime becomes non-homogeneous, with rapid quantum fluctuations of geometry. The correct description of such a structure should be quantum theory of gravity and construction of such a theory is one of the biggest challenges in theoretical physics. Quantum theory of gravity should at the same time explain the macroscopic four-dimensional geometry of the universe, described by the general theory of relativity. In this article a possible construction of such a theory, based on the method of causal dynamical triangulations, is discussed. This theory gave for the first time a description which connects the short-distance quantum effects with a correct long-range asymptotics. Preliminary results obtained for a model of ,,pure gravity" without matter are discussed. Even this simple version of the model predicts instability, leading to the Big Bang, and a four-dimensional universe on a macroscopic scale.
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