Masafumi Fukuma, Yuho Sakatani, Sotaro Sugishita
de Sitter space is known to have a thermal character. This can be best seen by an Unruh-DeWitt detector which stays in the Poincare patch and interacts with a scalar field in the Bunch-Davies vacuum. However, since the Bunch-Davies vacuum is the ground state only at the infinite past, if the scalar field starts in the vacuum state at a finite time, an Unruh-DeWitt detector then will feel as if it is in a medium that is not in thermodynamic equilibrium and that undergoes a relaxation to the equilibrium corresponding to the Bunch-Davies vacuum. In this paper, we first develop a general framework to treat such circumstances and write down the master equation which completely describes the finite time evolution of the density matrix of an Unruh-DeWitt detector in arbitrary background geometry. We then apply this framework to an ideal detector in de Sitter space which can get adjusted to its environment instantaneously, and show that the density distribution of the detector certainly exhibits a relaxation to the Gibbs distribution with the universal relaxation time of half the curvature radius of de Sitter space. This relaxation time gives the first example of such quantities that are related to nonequilibrium dynamics intrinsic to de Sitter space.
View original:
http://arxiv.org/abs/1305.0256
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