Infinite ethics
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.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.
Arntzenius, Frank (2014) Utilitarianism, decision theory and eternity, Philosophical Perspectives, vol. 28, pp. 31–58.
Askell, Amanda (2018) Pareto Principles in Infinite Ethics, PhD thesis, New York University.
Bostrom, Nick (2016) Infinite ethics, Analysis and metaphysicsMetaphysics, vol. 10, pp. 9–59.
An in-depth discussion of the potential moral implications of an infinite universe.
Center on Long-Term Risk (2020) Infinity in ethics, Center on Long-Term Risk.
Tomasik, Brian (2014) Should we believe in infinity?, Essays on Reducing Suffering, December 15 (updated 26 October 2018).
Treutlein, Johannes (2018) A wager against Solomonoff induction, The Universe From an Intentional Stance, March 31.
West, Ben (2015) Problems and solutions in infinite ethics, Effective Altruism Forum, January 1.
Wiblin, Robert & Keiran Harris (2018) Tackling the ethics of infinity, being clueless about the effects of our actions, and having moral empathy for intellectual adversaries, with philosopher Dr Amanda Askell, 80,000 Hours, September 11.
I really like the description, but would like to add that infinities in the "size" of the universe could also refer to time: it might be that there is an infinite future which we could possibly influence even if the size of the universe is finite. I don't think that anyone expects this to be true with anything approaching certainty (due to entropy it seems likely that there is no possibility to sustain life/agents indefinitely), but it does not seem ruled out to me that there could be relevant loopholes like cosmic expansion ensuring that entropy can just grow indefinitely or other unusual scenarios (like the possibility to create a pocket universe by triggering a big bang)).