You are assuming that the expansion of the universe consists in matter moving further apart in pre-existing empty space.
Rather it consists in the volume of space increasing over time. It’s hard to imagine it with space being three-dimensional, but down a dimension, space should be thought of not as 3-dimensional analog of an infinite plane, but of a closed surface (for simplicity, the surface of a sphere, say), which is increasing in area (volume in the 3D case) over time (like a balloon being blown up). What you say about accelerations and forces is about dynamics of matter within space (on the surface of the sphere in the dimension reduced analog) not about the dynamics of space itself.
That is an inference you made. Conceive of space however you want. That doesn't change the facts of observation. The universe is expanding at an increasing velocity. That means a force is accelerating it. Hence the need to theorize the existence of dark matter and dark energy.