If we consider the universe as a system, is there any net external force acting on it? I am thinking of whether or not the center of mass of the system moves. If there is no such a net external force then the center of mass of our universe must not move. Is it correct?
As a result, this center of mass can then be used as an absolute inertial frame of reference.
The universe has no center. It also doesn't have a center of mass.
The notion of "a force exerted on the universe" would need the universe to be able to move somewhere, since that's what forces (classically) do - they move things. But the universe is all there is, including spacetime, and the notion of "spacetime moving somewhere" is ill-defined.
Rather tautologically, the universe is "all that there is" - if the were a notion of force on it, there would be a notion of something exerting it on it, and hence, there would be more than just the universe, which contradicts the meaning of universe in the first place.
No matter what kind of word games you are going to play, there isn't some (measurable, for the axiomatic, superfluous alternative, see Lorentz aether theory) absolute reference frame. Special and general relativity are self-consistent, well-tested physical theories.
