The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility

Details The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility The volume of causal diamonds, asymptotically de Sitter space-times and irreversibility

2008-12-17

arxiv.org/abs/0812.3410v2

JHEP 0902:022,2009

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, no figures; v.2: conjecture 1 on p. 11 made more precise; version published in jhep

Scientific paper

10.1088/1126-6708/2009/02/022

In this note we prove that the volume of a causal diamond associated with an inertial observer in asymptotically de Sitter 4-dimensional space-time is monotonically increasing function of cosmological time. The asymptotic value of the volume is that of in maximally symmetric de Sitter space-time. The monotonic property of the volume is checked in two cases: in vacuum and in the presence of a massless scalar field. In vacuum, the volume flow (with respect to cosmological time) asymptotically vanishes if and only if future space-like infinity is 3-manifold of constant curvature. The volume flow thus represents irreversibility of asymptotic evolution in spacetimes with positive cosmological constant.

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