Is there a theory that proposes the universe is a spacetime bubble within a higher dimensional reality? I have heard that one proposal/interpretation of string theory is that, perhaps, extra dimensions exist at minuscule scales. I would conjecture that it is possible for the opposite to be true, akin to a bubble in water. The universe is the bubble, and the vast ocean around it is the higher dimensional space time. I would assume that there is some sort of  dimensional barrier (like the 2d surface of a 3d sphere perhaps, our universe being the sphere)
But past that surface would be the rest of whatever "else" is not bound by our universe. Meaning that theoretically the higher dimensional space is full of energy, perhaps in new diverse or exotic forms, and perhaps physics function differently or not at all. That being said I am proposing this for personal reasons, as I have a pipe dream of a concept, in the same sense  alcubierre drive is a pipe dream (please pardon that term).
That being said I was hoping to be aware of any and all theories that seem to have some potential to actually apply to the reality we live in, even if like string theory it may prove to be beautiful but un-testable (or so I have heard).
That being said I really have a hard time describing what it is I'm looking for, so the above was my best attempt at being descriptive. Unfortunately my college education is currently composed of 0 hours of college, but that will be changing for me this late August. That being said I have had a hard time searching for a theory online that matches what I am talking about, likely do to lack of proper terminology, as well as I feel it may be unlikely that i would find such theories or proposals outside of a science journal somewhere to begin with.
Just looking for a theory (or theories) that can or do support that sort of "bubble" universe, and has a mathematical formulation as well.
 A: An idea like yours was seriously proposed in the late 1990s as an explanation for the "hierarchy problem," which is the observation that the three fundamental forces which have working quantum field theories (electromagnetism and the strong and weak nuclear forces) have similar coupling constants at high energy, while gravity is much weaker.  The suggestion was that the interaction energies for the QFT forces are confined to the surface ("membrane" or "brane") on which we live, while gravity's energy mostly leaks out into the "bulk," making gravity appear weaker than it actually is.
This proposal made the testable prediction that there would be deviations from the $1/r^2$ behavior of the gravitational interaction at short distances --- which was exciting, because at the time no one had tried to measure purely gravitational interactions between objects closer than several centimeters apart. There was a flurry of experimental activity which revealed ... that Newtonian gravity totally describes interactions down to distances of tens of microns, ruling out all of the large-extra-dimension models people have been able to come up with.
For a summary of these ideas which predates the experiments that ruled them out, you might read Greene's Elegant Universe. Unfortunately I don't have a similar pop-science reference for the situation after the new experimental data appeared; by that time I was far enough along in my career that I was learning things from primary sources, which doesn't sound like what you want. Perhaps someone else will chime in with a better reading recommendation.
