Dmitri Krioukov, Maksim Kitsak, Robert S. Sinkovits, David Rideout, David Meyer, Marian Boguna
Causal sets are an approach to quantum gravity in which the causal structure of spacetime plays a fundamental role. The causal set is a quantum network which underlies the fabric of spacetime. The nodes in this network are tiny quanta of spacetime, with two such quanta connected if they are causally related. Here we show that the structure of these networks in de Sitter spacetime, such as our accelerating universe, is remarkably similar to the structure of complex networks -- the brain or the Internet, for example. Specifically, we show that the node degree distribution of causal sets in de Sitter spacetime is described by a power law with exponent 2, similar to many complex networks. Quantifying the differences between the causal set structure in de Sitter spacetime and in the real universe, we find that since the universe today is relatively young, its power-law exponent is not 2 but 3/4, yet exponent 2 is currently emerging. Finally, we show that as a consequence of a simple geometric duality, the growth dynamics of complex networks and de Sitter causal sets are asymptotically identical. These findings suggest that unexpectedly similar mechanisms may shape the large-scale structure and dynamics of complex systems as different as the brain, the Internet, and the universe.
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http://arxiv.org/abs/1203.2109
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