In The Hidden Reality, Brian Greene describes the bubble universes that would arise from inflation as being spatially infinite as observed by a viewer on the inside of the universe, yet spatially finite when observed by a viewer on the outside of the universe. What is the intuition for this?
I'll try to paraphrase his explanation to the best of my (clearly limited) understanding. He explains that each of these observers — one inside the bubble universe, and one outside — takes their cosmic metric of time to be the value of the inflaton field, such that points in space that have the same value of the inflaton field are, for that observer, at the same age. To an outside observer, the bubble universe is expanding, and the value of the inflaton in the "middle" of the bubble is decreasing over time. My best understanding of the argument for the inside observer's perception is that if we focus on any given concentric sphere of the bubble universe (e.g., its "edge" in the language of the outside observer), the inside observer always perceives all points on this sphere as always being at the same inflaton field value and therefore at the same age. Therefore this observer perceives the bubble universe to be infinite?