Second, we want to work with concepts in String Theory and M-Theory. Atoms are made of protons, neutrons and electrons. Each of those quantum particles, as well as others, can be described as manifestations of a vibrating superstring, like a violin string. String theory states that fundamental quantum particles can be described as 10D open superstrings called fermions. Bosons are closed superstrings, like rubber bands, that implement forces and vibrate in 26 dimensions. Don't worry about the number of dimensions right now. M-theory can be called membrane theory. The idea of membrane theory is that these open ended supstrings, fermions, will want to connect to the surface of a membrane. Membranes can be referred to a p-branes or d-branes; p refers to space with an odd number of dimensions; d refers to a space with an even number of dimensions. Our universe has a three dimensional space so it is referred to as a p3-brane. This p3-brane is represented as the 2D surface of the rubber balloon. Superstrings would stick to its surface and become our quantum particles. Arguably, a balloon as a D2-brane, but we're just trying to clarify these concepts. One could also say that the p3-brane coincides with empty space. The superstrings that stick to it are just the quantum particles that exist in our space.
In the balloon example, the air inside of the balloon will correspond to the Cosmological constant. Albert Einstein proposed this constant as a way to make the universe static. It was later discovered that the universe was expanding, so the universal wasn't necessary. However, that same constant can be used to moderate the expansion or contraction of the universe. By extrapolation, the following is being added. The Cosmolgical pressure is a hyperdimensional superfluid, an aether that exerts pressure against the p3-brane and causes it to expand; the exact mechanism is unknown at this time. The superfluid appears to spontaneously emerge from within the p3-brane. The pressure that it exerts causes the fluid to pass through the p3-brane to the outside of the brane. The difference in pressure will manifest as energy density in that region of space.
The idea of a "particle-space" relationship comes in handy in hyperdim physics. Basically, a particle is subject to the laws of physics and forces within the space that it occupies. In turn, a region of space can be described as a particle within a higher dimensional space.
A particle-space allows us to describe the laws of motion of a local space within a higher dimensional space. For example, in a spaceship with FTL (faster than light) capability, the very space around the spacecraft is artificial and fabricated. The spaceship, as it accelerates, will appear to vanish from our universe. It has slipped into an isolated space of its own. That space acts like a particle within a higher dimensional space, in which the laws of motion allow faster than light travel.