Could our universe be like a "fish tank" inside a higher dimensional reality? [duplicate]

I am a layperson with a strong interest in physics, so I may be using some terminology incorrectly. I am trying to understand whether the following analogy has any basis in actual physics. Imagine a fish living inside a fish tank. The fish experiences the tank as its entire environment. It can observe and move around within the tank, but it cannot perceive the room outside the tank in the same way that a person outside the tank can. Could something analogous be true of our universe? As I understand it, our universe is described by four-dimensional spacetime — three dimensions of space and one of time. Could our 4-dimensional spacetime similarly be part of, or embedded within, a higher-dimensional reality that we cannot directly perceive? If such an additional dimension existed, could it have observable effects within our 4-dimensional spacetime? For example, could gravity provide a possible way of detecting it? Are there established physical theories that describe our universe as something like a lower-dimensional part of a higher-dimensional space? I am not asking whether parallel universes exist in science fiction. I am trying to understand whether the intuition behind my fish-tank analogy has any basis in actual physics. I would appreciate an explanation suitable for someone without a formal background in physics