Abstract
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 settlement disappears due to vacuum decay. We study in detail the collective life expectancy of two comoving objects in de Sitter space as a function of the initial separation, the horizon radius and the vacuum decay rate. We find that even with a modest initial separation, the collective life expectancy can reach a value close to the maximum possible value of 1.5 times that of the individual object if the decay rate is less than 1% of the expansion rate. Our analysis can be generalized to any number of objects, general trajectories not necessarily at rest in the comoving coordinates and general FRW space-time. As part of our analysis we find that in the current state of the universe dominated by matter and cosmological constant, the vacuum decay rate is increasing as a function of time due to accelerated expansion of the volume of the past light cone. Present decay rate is about 3.7 times larger than the average decay rate in the past and the final decay rate in the cosmological constant dominated epoch will be about 56 times larger than the average decay rate in the past. This considerably weakens the lower bound on the half-life of our universe based on its current age.
Highlights
The decay of a metastable vacuum proceeds via bubble nucleation [1,2,3,4,5,6]
It has been known for quite some time that in de Sitter space if the expansion rate of the universe exceeds the decay rate due to phase transition even collectively the bubbles of stable vacuum cannot fill the whole space [15] and there will always be regions which will continue to exist in the metastable vacuum
For two objects we obtain explicit expression for the life expectancy in terms of three parameters: the Hubble 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
Summary
Let us suppose that we have two independent objects, each with a decay rate of c per unit time. Of this the probability that the second object exists after time t is given by exp[−c t] and it has the same life expectancy. To compute this note that since the two objects are independent, the probability that both will decay by time t is given by (1 − P1(t))(1 − P2(t)) = (1 − P1(t)). At t = 0 we have τ = −1 and comoving distances coincide with the physical distances We shall use this space-time as a toy model for studying the kinematics of vacuum decay. We shall not explore how such a bubble is produced; instead our goal will be to study its effect on the life expectancy of the objects living in this space.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
