From Eternity to Here

by Sean Carroll

The question that any modern theory of cosmology must therefore answer is: Why don’t we live in de Sitter space? It has a high entropy, it lasts forever, and the curvature of spacetime induces a small but nonzero temperature. De Sitter space is empty apart from the thin background of thermal radiation, so for the most part it is completely inhospitable to life; there is no arrow of time, since it’s in thermal equilibrium. There will be thermal fluctuations, just as we would expect in a sealed box of gas in a Newtonian spacetime. Such fluctuations can give rise to Boltzmann brains, or entire galaxies, or whatever other macrostate you have in mind, if you wait long enough. But we do not appear to be such a fluctuation—if we were, the world around us would be as high entropy as it could possibly get, which it clearly is not. There is a way out: De Sitter space might not simply stretch on for all eternity, uninterrupted. Something might happen to it. If that were the case, everything we have said about Boltzmann brains would be out the window. That argument made sense only because we knew exactly what kind of system we were dealing with—a gas at a fixed temperature—and we knew that it would last forever, so that even very improbable events would eventually occur, and we could reliably calculate the relative frequencies of different unreliable events. If we introduce complications into that picture, all bets are off. (Most bets, anyway.)