As mentioned in the comments, Science Fiction writers, led by the mathematician Charles Howard Hinton, explored the consequences of the fact that the mathematical theory of space can be extended to dimensions of number greater than the 3 we see around us. If one could "access", "manipulate" or "travel" in a fourth dimension, i.e. one independent of the three we can directly experience, you would be moving through a form of space which is exactly like what we mean by "parallel universe" - as people in the 'regular' universe would be unable to witness any changes that took place there, and yet 'real' physical interactions and experiences could happen solely in that extra dimension. A good way of accessing an intuition about this is imagine if everything that went on in a room was projected onto a wall - say an observer is outside a marquee or tent and sees the shadows on the wall. Then if people move toward or away from the wall the observer won't see (much of)* a change, so any interactions that happen in that dimension - the dimension perpendicular to the wall - happen in a world inaccessible to the observer - just like being in a 'parallel universe'.
It's fascinating that this question has come up as within the last couple of weeks I have read both a review of a novel about Hinton https://www.theguardian.com/books/2020/apr/23/hinton-by-mark-blacklock-review-voyages-into-the-fourth-dimension and an article by the author of that novel about the fourth dimesnion in science fiction https://www.theguardian.com/books/2020/jun/03/top-10-four-dimensional-novels-mark-blacklock-hinton.
- the 'projection' in this real-life example doesn't work like a perfect mathematical projection, but I hope you still see the point
