This question is related to Weak Equivalence Principle. Is the earth actually expanding at a rate 9.8 ms-2, which is exactly countered by gravitational space expansion (g_rr term in Schwartzchild Metric)? Or it just acts as though it is expading, meaning it just expands space and slows down time (curves spacetime to be precise) so that the geodesic of a falling apple goes downwards?
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Exercise: with such acceleration, how long would it take to expand to Earth's present measured radius from a point? Not long, is it? – J.G. Nov 13 '21 at 14:07
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1It won't actually expand if it’s cancelled by the space getting bigger. – Nayeem1 Nov 13 '21 at 14:29
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I wouldn't use the word "swelling," because that suggests a change of size (which isn't happening), but you could say it like this: The earth's surface is accelerating outward at $9.8$ m/s$^2$, and the curvature of spacetime is the reason that outward acceleration does not cause any swelling. In this statement, the word "acceleration" refers to absolute acceleration (the kind that can be measured inside a tiny box with no windows), not relative acceleration (which requires looking out the window and would contradict the not-swelling property). – Chiral Anomaly Nov 13 '21 at 15:06