Not only the universe is expanding. All matter expands continuously. This expansion causes acceleration from objects on the surface of big objects. We experience this as gravitation. Connecting the Lorentz-transformation with the fall acceleration (9,8 m/s) the speed of the visible part of our universe is calculated to be 12278 m/s2 related to a primary universal inertial reference frame.
At this moment there is no alternative theory to gravitation that is broadly accepted as scientific valuable. Probably we need some elements of different theories to put together. Some parts to combine, some parts to throw away, some parts to change. There must be something that we overlooked until now. Let's rethink gravitation.