Hi Ascending One, I can help you.
Its a consequence of Einsteins Equations. Matter an energy couple to spacetime generating expansion...its as as simple as that.
Formally the metric for an FRW universe reads (in cartesian coordinates)
[tex]ds^2=dt^2-a^2(t)(dx^2+dy^2+dz^2)[/tex]
The expansion of the universe is 'controlled' by the scale factor a(t). To find a(t) you need to solve Einsteins equation:
[tex]G_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}[/tex]
This is pretty easy actually. Anyhow, you discover that a(t) is related to the energy density and pressure of the universe if you model it as a perfect fluid. Some fiddling with conservation of energy equations demonstrate that the pressure is negative which drives the expanding (accelerated) universe.
Summary - Forget what you know about forces and basic classical mechanics, matter and energy couple to spacetime and generate expansion. Thats it. I'm sorry of you find this hard to visualize or understand mechanically, but sadly general relativity is not really like that. That was Einsteins genius.