By F. Adams, G. Laughlin
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Extra resources for A Dying Universe - Long-Term Fate of Astrophys. Objects [lg article]
35]. If the vacuum energy density provides any appreciable fraction of the total energy density at the present epoch (in other words, if ν is not too small), then the universe will enter an inflationary phase in the very near future. Furthermore, almost any nonvanishing value of the present day vacuum energy will lead the universe into an inflationary phase on the long time scales considered in this paper. For small values of the ratio ν, the future inflationary epoch occurs at the cosmological decade given by ηinflate ≈ 10 + 1 1 .
In constructing this table, representative values for the (often uncertain) parameters have been assumed; the stated time scales must therefore be viewed as approximate. Furthermore, as a general rule, both the overall future of the universe, as well as the time line suggested in Table I, become more and more uncertain in the face of successively deeper extrapolations into time. Some of the effects we have described will compete with one another, and hence not all the relevant physical processes can proceed to completion.
The fraction ∆∞ will generally be much smaller than this example. The fact that the fraction ∆∞ is finite implies that the process of particle annihilation can provide only a finite amount of energy over the infinite time interval η1 < η < ∞. 3. Formation and Decay of Positronium Another related process that will occur on long time scales is the formation and eventual decay of positronium. This process has been studied in some detail by Page & McKee (1981ab; see also the discussion of Barrow & Tipler, 1986); here we briefly summarize their results.