The possibility that the universe is infinite, and that it might therefore contain an infinite number of morally relevant beings, is a challenge to moral theories that instruct us to increase the good in the world. Briefly, the trouble is that in an infinite universe the amount of good may be infinite no matter what we do, and it is difficult to compare infinities.
Cosmologists commonly regard the universe as infinite in their models. However, this is partly for mathematical simplicity, and there is also an alternative hypothesis: It is possible that the universe “curls in on itself,” in the same way that the two-dimensional surface of the Earth does, such that traveling far enough in any one direction would ultimately bring you back to where you started.
The present situation, roughly, is that an infinite universe would be consistent with all of the data that cosmologists currently have available to them, but it is very difficult to discern the difference between a space that is infinite and a space that is simply enormously big. There is no widely accepted probability that one or the other hypothesis is true.
It is also important to note that a universe could be infinite without also containing infinite value. For instance, an infinite universe which contained only a finite number of life-harboring regions would not pose a problem to aggregative moral theories. However, cosmological evidence points strongly toward the universe also being “uniform,” which means that all sufficiently large-scale regions should have approximately the same properties, including the ability to harbor life.
Bostrom, Nick. 2011. Infinite ethics. Analysis and metaphysics 10: 9-59.
An in-depth discussion of the potential moral implications of an infinite universe.