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Katie Mack
@astrokatie.com

Okay so parallel universes are not really a thing in physics unless you’re talking about the Everett Many Worlds interpretation of quantum mechanics in which case you should be looking for people who write about quantum foundations. But that’s not related to extra dimensions (of space).

Katie Mack
@astrokatie.com

Extra dimensions certainly come up in string theory, so you can look for books on that. There are extra dimensional theories built around trying to explain the weakness of gravity or solve the hierarchy problem; you can look up Kaluza-Klein theory, “large extra dimensions”, or “brane world” models.