Yes, it a certain sense one could say that the universe and everything in it is in constant motion.

Consider, for simplicity, a point-like particle - in space-time, such a particle is a twisting, curving, but static world-line. Now, the thing is that at

**every** point along that world-line one can define what is called a unit tangent-vector; the means we have a 4-vector which is tangent to the world-line at that point, and the components of which are parametrized in terms of the arc-length of the world-line. When you examine the magnitude ( "length" ) of such a vector, you will find that it is always exactly c, i.e. the speed of light, at all points; the direction of the vector will be a combination of "space" and "time" elements. For example, for a particle perceived to be at rest the vector may point only in the time direction ( "ageing" ); for something going very fast it may point a lot more in the "space" directions than it does in the time direction ( "time dilation" ), relative to the first event; and so on. The point is that a case can be made for everything in space-time to have a velocity of exactly

*c* at all times, i.e. for the universe to be in constant motion, based on purely geometric considerations. This works in both flat as well as curved space-times.

Not sure if that makes sense, but hopefully you get the main idea