As for the inflation of the universe, it's not really movement with kinetic energy/momentum, it's more like changing a parameter that guides the universe. Like changing a universal constant, like speed of light in vacuum.
However, my theory is that inflation of the universe is a "local" phenomena in time-space, caused by the big bang. Lots of matter (the whole universe as it was born) moved rapidly outward at the time, thus it must've created a tremendous gravitational wave and anything floating in space right now (i.e. stars) is like oil on top the ocean. Imagine you dropped a kiloton of oil condensed into a cubic millimeter on the surface of the ocean. A kiloton is a kiloton and would make huge waves, and oil would float on the surface and spreading all over the place at high speed, just like the big bang. And what happens to the distance of floating drops of oil?
I believe something alike is happening to the universe.