Surviving in a Metastable de Sitter Space-Time

TL;DR

This paper examines how civilizations in a metastable de Sitter universe can extend their collective survival by spreading out, analyzing the impact of initial separation and decay rates on their lifespan, with implications for the universe's stability.

Contribution

It provides a detailed analysis of the collective life expectancy of objects in de Sitter space and generalizes the results to various trajectories and space-times.

Findings

Collective life expectancy can approach 1.5 times that of a single object with low decay rates.

Current vacuum decay rate is increasing over time due to accelerated cosmic expansion.

The lower bound on the universe's half-life is significantly weakened by the increasing decay rate.

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.