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# A comoving object in de Sitter space and its past light cones at conformal times τ and τ + δτ.

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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...

## Contexts in source publication

Context 1
... a single object in de Sitter space at rest in the comoving coordinate x (say at x = 0), shown by the vertical dashed line in Fig. 3. We start at t = 0 (τ = −1) and are interested in calculating the probability that it survives at least till conformal time τ. If we denote this by P 0 (τ) then the probability that it will decay between τ and τ + δτ is −P 0 (τ)δτ where denotes derivative with respect to τ. On the other hand this probability is also given by the ...
Context 2
... we denote this by P 0 (τ) then the probability that it will decay between τ and τ + δτ is −P 0 (τ)δτ where denotes derivative with respect to τ. On the other hand this probability is also given by the product of P 0 (τ) and the probability that a vacuum bubble is produced somewhere in the past light cone of the object between τ and τ + δτ, as shown in Fig.3. The volume of the past light cone of this interval can be easily calculated to be Therefore, if K is the probability of producing the bubble per unit space-time volume then the probability of producing a bubble in the past light cone of the object between τ and τ + δτ is given by −2Kδτ/τ. ...
Context 3
... consider the case of an isolated object. The calculation proceeds as in §3.1. However, in computing the volume of the past light cone in Fig. 3 we have to take into account the fact that for each σ, the light cone is a sphere of radius (τ − σ). Since the coordinate radius of the sphere is (τ − σ) and the space-time volume element scales as 1/σ 4 we get the volume of the past light cone of the object between τ and τ + δτ to ...

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... the number of membranes that hit an observer per unit time. We will now do so by geometric means, as in [37]. ...
... This equation gives the probability that a bubble which was born at conformal time τ 0 actually makes it to conformal time τ (see [37]). In terms of proper time, we have ...
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