Does anyone know if there is a difference between the affectable and the accessible universe? Are they the same?

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The observable universe is different from, and its radius is about three times bigger than the affectable universe. You can read more in the following paper, abstract below: Ord, Toby. "The edges of our universe." arXiv preprint arXiv:2104.01191 (2021).

This paper explores the fundamental causal limits on how much of the universe we can observe or affect. It distinguishes four principal regions: the affectable universe, the observable universe, the eventually observable universe, and the ultimately observable universe. It then shows how these (and other) causal limits set physical bounds on what spacefaring civilisations could achieve over the longterm future.

Toby Ord explains several related distinctions very clearly in his paper 'The Edges of Our Universe'. Highly recommended: https://arxiv.org/abs/2104.01191

Not sure if it's the widely used definition, but I think of affectable as anything in our future light cone, with accessible as just the bits which we could get something (e.g. a von Neumann probe) physically to before the expansion of the universe takes it away from our reach, which is a smaller bubble because we can't send matter at light speed, our probe would have to slow down at the other end, and the expansion of the universe robs our probe of velocity relative to distant galaxies over very long periods.

Edit: The FHI has a relevant paper: https://www.fhi.ox.ac.uk/wp-content/uploads/space-races-settling.pdf