The understanding I have of the fundamental forces of the universe has advanced a bit, so I thought I'd share. To my understanding, the fundamental forces are simple and elegant. Momentum and gravity and 'dark energy' are all related. 'Dark matter' may be an emergent property of these forces. I've got just about everything here, in one nice, neat, relatively simple package.
Here is a crudely drawn picture of what I'm going to be talking about.
Matter draws its energy from this field. The field adjusts by lowering the energy level around the particle of matter, with the amount of drop decreasing in a square law fashion. This is gravity. All things seek to occupy a lower energy level, and require force to make them go up the energy gradient. They gain energy by going down the gradient.
This is the slanted black line above. Gravity is a push from empty space, more than a pull from matter. Gravity is a lower energy level.
Momentum is a directional wave in the ambient energy, with the lower end of the wave in the direction of movement. Above, it is shown as the red curve. In reality, it is three dimensional, with relative null points at 90 degrees to forward motion. (Think of a slanted bowl.) Thus, particles are forced forward towards to lower energy level, and resist going backwards towards the higher energy level. This also explains the red and blue shift of emitted photons - they gain energy if going forwards, are neutral at 90 degrees to motion, and lose energy if emitted backwards.
The blue dot at the center is the particle, whatever it may be. The wave around it is its momentum - the higher the momentum, the steeper and more narrow the curve. More massive particles require more energy to influence their momentum wave. This implies that their waves have a shorter wavelength, which matches with observations. The more massive and faster a particle is, the more fixed its location is - the shorter its position wavelength. Remember, shorter wavelengths require more energy.
Here's the really cool part - space-time dilation is built into the picture. Using natural units (speed of light equals 1, no time/space dilation equals 1), the sine of the angle is the velocity, and the cosine of the angle is perceived time and length. Thus, a theoretical non-moving particle in an area of no gravity (no energy differentials at all) would have a perfectly flat wave (nonexistent, really) with sine 0 and cosine 1. This is the fastest possible perception of time and distance (1), and the slowest possible speed (0). Conversely, a photon's momentum wave is a verticle discontinuity of width zero. It has a sine of 1 (fastest possible velocity) and a cosine of 0 (lowest possible perception of time and distance). All of a photon's energy is in its spin, not its forward movement.
The edge of a black hole would be where the energy gradient is at 90 degrees to the vertical, and would be where the total energy level reaches zero. What's beyond that? Negative energy levels, with weird results. There be dragons.
So, the universal energy accounts for dark energy. It pushes matter away from it, the more you have of it. So that checks out. The fun question is - as the universe expands, does this energy level drop, or is it created out of nothing? According to the recent research I've seen, it seems to stay steady, appearing out of nothing. This violates the principle of conservation of energy on a large scale, but not so much at the local level. So the universe isn't a pot of water, with the level going down as the pot grows larger. It seems to be more of a sieve in a larger pool of water, with the level staying steady even as the vessel grows larger.
Here's where things get speculative. Imagine that the energy acts as a fluid. Yes, it can move on its own. That's where gravity waves come from, and the apparent existence of dark matter. If the energy field is a fluid, it can and does move. This movement is caused entirely by the existence and movement of matter, which we see as gravity. The fluid energy wouldn't move at any scale we would perceive, but it would have large scale movement. Say, with the steady spin of a spiral galaxy. The matter in a proto-galaxy would begin to coalesce and spin. That causes the emergence of the spiral arm structure. After a bit of resistance, the fluid energy would also begin to spin, eventually keeping up with the matter. This fixes the spin of the arms like a record player. The entire construct would spin like a record, with fixed axial rotation, instead of like water going down a drain.
To see this in action, fill a pot of water. Sprinkle herbs on top. Now, stick a spoon in the center of the pot and twirl it. The herbs will spin around, faster and faster at the center, forming spirals. The spirals will eventually stabilize as the entire pot of water eventually moves at a fixed axial rate of rotation.
Again, this part is speculative, but seems to agree with observations and basic principles.
Oh, and light speed limits don't apply to spin, just momentum. They also don't seem to apply to the ambient energy levels, just the particles in them. Gravity works instantly, across the entire galaxy, ignoring all limits. Waves in the energy, however, must respect the speed limit.
Why no, I can't even begin to express this mathematically. I don't think in math. I think in pictures, and thus geometry. (I choked at three dimensional calculus. I couldn't see the shapes described by the equations.)
Math is just a description of what geometry is doing, anyways. It's the geometry that is fundamental. If you don't believe that, go back over the fundamental theorems of calculus - differentiation is computing the slope of a curve, and integration is computing the area under a curve. The curve is fundamental, and may be described and analyzed with mathematics.