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The figure showing the 'gain' in the life expectancy for two objects compared to that of one object as a function of T for r = .0003, .001, .003, .01, .03, .1 and .3.

The figure showing the 'gain' in the life expectancy for two objects compared to that of one object as a function of T for r = .0003, .001, .003, .01, .03, .1 and .3.

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Article
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In a metastable de Sitter space any object has a finite life expectancy beyond which it undergoes vacuum decay. However, by spreading into different parts of the universe which will fall out of causal contact of each other in future, a civilization can increase its collective life expectancy, defined as the average time after which the last settlem...

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Context 1
... constant H of the de Sitter space-time determined by the cosmological constant, the vacuum decay rate or equivalently the life expectancy T of a single isolated object and the initial separation r between the two objects. In fact due to dimensional reasons the result depends only on the combination HT and Hr, so we work by setting H = 1. In Fig. 1 we have shown the result for the ratio of the life expectancy of two objects to that of a single object -called the 'gain' -as a function of T for different choices of r. From this we see that even for a modest value of r = 3 × 10 −4 the gain in the life expectancy reaches close to the maximum possible value of 1.5 if T is larger that ...
Context 2
... denote this by P 12 (t). This is given by the sum of the probability that C 1 survives till time t and the probability that C 2 survives till time t, but we have to subtract from it the probability that both C 1 and C 2 survive till time t since this will be counted twice otherwise. This can be seen from the Venn diagram of two objects shown in Fig. 10. ...
Context 3
... in the 1+1 dimensional case, ¯ t 1 is slightly larger than T but this is simply due to the choice of initial condition that both observers are assumed to exist at t = 0. In Fig. 11 we have plotted the ratio ¯ t 1 /T as a function of T for various values of r, and as we can see the result remains close to 1. More discussion on ¯ t 1 can be found below (4.23). Next we consider the generalization of (3.18)-(3.22). The analysis is straightforward and we get the ...
Context 4
... can be checked using (4.11), (4.12), (4.16) and (4.18) that for r → 0 we get ¯ t 12 / ¯ t 1 = 1 and for T → ∞ we get ¯ t 12 / ¯ t 1 = 3/2. The values of 'gain' ≡ ¯ t 12 / ¯ t 1 for different values of r have been plotted against T in Fig. ...
Context 5
... numerical values of A(T ) are moderate -for example A(5) 0.439 and A(10) 0.457. A plot of A(T ) as a function of T has been shown in Fig. 12. The 1/T exponent of r shows that even if we begin with small r, for moderately large T (say T ∼ 5) we can get moderate enhancement in life ...
Context 6
... quantity of direct interest is the probability P 123 (t) that at least one of the objects survives till time t. With the help of the Venn diagram given in Fig. 13 we get P 123 (t) = P 1 (t) + P 2 (t) + P 3 (t) − P 12 (t, t) − P 13 (t, t) − P 23 (t, t) + P 123 (t, t, t) ...
Context 7
... this we can calculate the life expectancy of the combined system as Figure 13: The Venn diagram illustrating that the survival probability of one of A, B or C, denoted by P (A ∪ B ∪ C), is given by ...
Context 8
... generalization involves considering a situation where multiple objects originate at the same space time point and then follow different trajectories, eventually settling down at different comoving coordinates. This has been illustrated in Fig. 14. This represents the realistic situation since by definition different civilizations of the same race must originate at some common source. We can now generalize our analysis to take into account the possibility of decay during the journey as well. Eqs.(5.3) and (5.4) still holds, but the computation ...

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Citations

... the number of membranes that hit an observer per unit time. We will now do so by geometric means, as in [37]. ...
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